Reconsideration of the Rheology of Silica Filled Natural Rubber

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Reconsideration of Rheology of Silica Filled Natural Rubber Compounds Yihu Song, Lingbin Zeng, and Qiang Zheng J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 18 May 2017 Downloaded from http://pubs.acs.org on May 23, 2017

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The Journal of Physical Chemistry

Reconsideration of Rheology of Silica Filled Natural Rubber Compounds

Yihu Song,a,* Lingbin Zeng,b Qiang Zhenga

a

MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of

Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, Hangzhou 310027, China b

Shanghai Aerospace System Engineering Institute, Shanghai 201110, China

ACS Paragon Plus Environment


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ABSTRACT:

There is substantial progress along with giant debate in reinforcement

mechanisms in relation to structured filler network and heterogeneously retarded polymer dynamics while the dissipation behaviors have never been clarified for nanoparticle filled polymers. Herein dynamic rheological behaviors of silica filled natural rubber were investigated. Master curves of linear rheology in the hydrodynamic regime and those of nonlinear Payne effect at a predetermined frequency were created, disclosing a leading role of dynamically retarded bulk rubbery phase to the hydrodynamic regime and a leading role of molecular disentanglement in the bulk phase to the Payne effect. The methodology is able to account for both reinforcement and dissipation of the compounds as a function of filler content. Furthermore, a frequency-dependent hydrodynamic to non-hydrodynamic transition is revealed, revealing the importance of the relaxation of chains in the bulk phase to both reinforcement and dissipation of the compounds. It is suggested that the dynamics of the bulk phase play a critical role for the rheology in the hydrodynamic regime while the fractal filler aggregates become dominative only in the terminal non-hydrodynamic regime where the bulk phase relaxes sufficiently.

2


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■ INTRODUCTION Nanoparticles significantly reinforce rubbers and cause a so-called fluid-to-solid transition characterized by large increases in complex modulus G*(ω,φ) and complex viscosity η*(ω,φ) at small strain amplitude γ and low frequencies ω with increasing filler volume fraction φ.1-4 The reinforcement is always accompanied with a nonlinear Payne effect appearing as an enormous G*(γ,φ) decay with increasing γ at given ω. Both the reinforcement and Payne effect are long standing topics receiving sustained interest from the scientific community.2-6 It is generally accepted that filler aggregating7-8 and networking9 mediated by filler-polymer interactions are important for both the reinforcement and rheological nonlinearity. The reinforcement has been ascribed to hydrodynamic effects induced by nanoparticles,3,

10-12

changes in the matrix properties close to the filler surface,13-16 and, in highly filled rubbers, formation of filler network.17 The latter is extensively treated in terms of percolation, jamming, soft glass, or gelation theories while conceptual conflicts and experimental discrepancies still exist.2, 4-5 For the Payne effect, it is ascribed to several processes, including but not limited to, agglomeration/ deagglomeration of aggregates,18-19 breakup/ reformation of filler network19-23 or polymer-filler network,19 and molecular disentanglement of bound/free rubber chains.1, 19, 24-25 The importance of chain immobilization to both reinforcement and rheological nonlinearity is emphasized.26-27 The reinforcement is expected to maximize when the rigid (glassy) immobilization layer percolates27-32 while the Payne effect occurs due to disentanglements in the bound-to-free rubber transition region,19, 33 desorption of chains from the filler surface26, 34 in the rigid layer,32 and yielding, softening and crazing of the glassy layer.28, 31 However, established theories usually ignore contributions of the bulk phase, formed by a population of chains being far away from the filler inclusions, to both reinforcement and the Payne effect. Furthermore, the filling-induced variation in dissipation of the compounds is never clarified. Accompanying filler structuring and chain adsorption, filling strongly slows down diffusion of global chains in the bulk phase.35-36 Besides the well-known retardation and even prohibition of reptation of chains adsorbed on the nanoparticle surface,37-40 quantifying the rheological role of 3



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the dynamically retarded chains in the bulk phase remains a quite charming and challenging topic. In this study, rheology of precipitated silica filled natural rubber (NR) compounds was thoroughly investigated with respect to silanes and φ. The fundamental mechanisms involving in polymer dynamics modification are discussed on the basis of a proposed method for creating master curves of linear rheology for the compounds in the hydrodynamic regime. The crucial role of the bulk phase to the Payne effect is disclosed based on creation of master curves of nonlinear rheology for the compounds at given ω.

■ EXPERIMENTAL SECTION Materials. Natural rubber (NR, SVR3L grade; density 0.92 g cm-3, polyisoprene content 98 %, weight-averaged molecular weight 1,120 kg mol-1, polydispersity index 3.57) was purchased from Shanghai Duokang Industrial Co. Ltd., China. Precipitated silica (ZQ356; silica content 97.3%, cetyltrimethyl ammonium bromide absorption 184 m2 g-1, dibutyl phthalate absorption 5.51 cm3 g-1) was purchased from Zhuzhou Xinglong Chem. Industrial Co. Ltd., Hunan, China. Silica forms aggregates by fused nanospheres of 15.6 nm in equivalent diameter estimated from specific surface area. Antioxidant N-(1,3-dimethylbutyl)-N'-phenyl-p-phenylenediamine was obtained from Changzhou

Xince

Polym.

Mater.

Co.

Ltd.,

China.

Silanes,

bis(γ-triethoxysilylpropyl)-tetrasulfide (TESPT) and (3-aminopropyl)triethoxysilane (KH550), were obtained from Hangzhou Jessica Chem. Co. Ltd., China. All the materials were used as received. Sample Preparation. Silica of 100 g and silanes of 8 g were premixed in a high-speed mixer (Wuhan Yiyang Plastic Machinery Co. Ltd., China) for 10 min. The compounds containing 1.6 phr (parts per hundred rubber) antioxidant were prepared at 50 °C by using a laboratory two-roll open mill (XK-160, Zhanjiang Rubber 4


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& Plastic Machinery Co. Ltd., China) according to a standard procedure elaborated in ASTM-D3192. The compounds were further mixed at 150 °C and 50 rpm for 10 min in a torque rheometer (XSS-300, Kechuang Rubber Plastic Mechanical Equipment Co. Ltd., China). For comparison, a silane-free compound containing 50 phr silica, named as Ref 1, was prepared following the same procedure. Another compound, Ref 2, was prepared by mixing rubber gum, silica (50 phr), TESPT (4 phr) and antioxidant (1.6 phr) simultaneously following ASTM-D319, which was further thermally treated at 150 °C for 30 min in a vacuum oven. The compounds were compressed into sheets of 2.0 mm in thickness on a press vulcanizer (XL-25, Huzhou Xinli Rubber Machinery Co. Ltd., China) at 100 ± 5 °C under 14.5 MPa for 10 min. The sheets were cut into discs of 25.0 mm in diameter. According to dynamic mechanical analysis, glass transition temperature of NR in the compounds is almost the same as that of pure NR because the nanoparticles may not influence the segmental dynamics17, 41-42 for chains far away from the nanoparticles. Characterizations. A strain-controlled rheometer (ARES-G2, TA Instrument, USA) was used to measure the linear and nonlinear dynamic rheological responses of the compounds at 100 °C. A plate-plate geometry was equipped with serrated surface texture to prevent slipping, which allowed measuring the rheology almost the same as the results using plates of smooth surface.17 All the specimens were equilibrated for 5 min before performing frequency (ω) sweeps from 100 to 0.01582 rad s-1 at strain amplitude (γ) of 0.1%. Strain amplitude sweeps from 0.01% to 100% were performed at ω = 1 rad s-1.

5



■ RESULTS AND DISCUSSION Linear Rheology. Figure 1 shows linear rheology of the compounds. At low frequencies, NR exhibits the typical terminal flow characterized by scaling laws of G'm(ω)~ω2 and G''m(ω)~ω1 accompanied with a sustained decay of tanδ as a function of ω. In the compounds, the ω-dependences of G'(ω,φ) and G''(ω,φ) weaken and the tanδ value especially in the low-ω zone decreases gradually with increasing φ. The TESPT- and KH550-containing compounds exhibit the so-called fluid-like [G'(ω,φ) < G''(ω,φ) in the low-ω zone] to solid-like [G'(ω,φ) > G''(ω,φ) in the low-ω zone] rheological transition43 at φ ≈ 0.077 and 0.040, respectively, where critical gel-like relations G'(ω,φ)≈G''(ω,φ)~ ω0.50 and G'(ω,φ)≈G''(ω,φ)~ω0.45 are manifested.44-46 This transition is accompanied with appearance of the tanδ peak to high frequency with increasing φ. For the compounds at φ = 0.172, the rheology demonstrates marked modulus plateaus depending on silane and processing technology. In comparison with the silane-free compounds (Ref 1), silanes could improve G' and lower tanδ and the effect of TESPT is more marked than KH550. For the TESPT-containing compounds, thermal treatment at static conditions (Ref 2) is more effective for improving G' and lowering tanδ than the internal mixing technology.

H(τ) (Pa)

0.172 (5) 10

10

108

0.142 (4)

104 102

102 100 -2 10

100

-1

102

ω (rad s )

0.111 (3)

106

10

102

4

101

0.5

tanδ

10mG', 10mG'' (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.077 (2) 0.040 (1)

ϕ=0 (m=0)

100

1

(a)

(b) 10 -2 10-1 -1 0 1 2 -2 -1 0 1 2 1 10 10 10 10 1010 10 10 10 10 2

0

-1

ω (rad s )

6


0.172 (5)

H(τ) (Pa)

1010

10mG', 10mG'' (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.142 (4)

108

0.111 (3)

106

0.077 (2) 0.040 (1)

4

102 100 -2 10

100

102

101

ω (rad s-1)

0.45

100

ϕ=0 (m=0)

10

102

104

tanδ

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1

(c) 2 (d) 100 -2 10-1 -1 0 1 2 -2 -1 0 1 2 1 10 10 10 10 1010 10 10 10 10 -1

ω (rad s ) Figure 1. Linear rheology for TESPT- (a and b) and KH550-containing compounds (c and d). (a and c) G' (solid symbols) and G'' (hollow symbols) and (b and d) tanδ as a function of ω. Also shown in (a) and (b) are the data of Ref 1 (pentagon) and Ref 2 (hexagon) for comparison. Insets in (b) and (d) show H(τ) as m

a function of τ. The data in (a) and (c) are vertically shifted by a factor of 10 and the thick and thin curves are drawn according to modified “two phase” model.

Insets in Figure 1 show relaxation time spectra H(τ) derived from dynamic modulus according to Tschoegl.47 It is found that H(τ) is elevated with increasing φ and the relaxation is retarded greatly at long relaxation times τ.48 The long-term retardation accompanying with lowering of tanδ and shifting of tanδ peak is associated with the formation of a filler structure having components with extended relaxation times.49 However, no integral relaxation peak belonging to the filler phase could be observed in weighted relaxation time spectra τH(τ) in the ω-range experimentally achieved (not shown).

Hydrodynamic to Non-Hydrodynamic Transition. The fluid-to-solid like transition has been previously assigned to slowdown of chain motion, adsorption of chains on the filler surface and formation of a percolating filler network throughout the rubbery matrix.2-5 All the highly filled compounds behave solid-like possibly due to incomplete relaxation of space-ﬁlling, self-similar filler network occurring simultaneously with relaxations of chains contacting with the filler50 and 7



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those in the bulk phase. The compounds are excepted to exhibit a physical gel rheology over a broad range of φ.51 At the gel point, the gel rheology following universal scaling laws G'(ω,φ)~G''(ω,φ)∼ωp and H(τ)~τ-p 44-46 is expected. Here, p is relaxation exponent lying between 0 and 1 and p = 0.5 is predicted52 for gels formed by soft spheres interconnected by flexible bonds.53 For the silica/NR compounds, p is located at 0.45-0.50, being in agreement with that found in fumed silica filled polyethyleneoxide.54 The critical concentration for the fluid-to-solid like transition is usually identified by the intersection of tanδ measured at diﬀerent frequencies as a function of φ.46, 55-57 This Winter-Chambon criterion is, however, clearly disobeyed for the compounds (Figure 2). Thus the gel-like relations found for φ ≈ 0.077 and 0.040 for the TESPTand KH550-containing compounds, respectively, could not define a true gelation point. The failure of the Winter-Chambon criterion suggests that the dynamics of the bulk phase should be considered when discussing the so-called fluid-to-solid like transition.

Figure 2. Tanδ against φ for TESPT- (a) and KH550-containing compounds (b) at ω ranging from 0.01582 rad s-1 to 100 rad s-1.

Relative storage modulus, R'(ω,φ)=G''(ω,φ)/G'm(ω), is usually used to discuss the reinforcement mechanism. The reinforcement at low φ has been attributed to hydrodynamic effects3 while that at high φ is usually discussed in terms of “jamming” or percolating network 8


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models.2-5 Figure 3a-b shows R'(ω,φ) at five prescribed frequencies as a function of φ for the TESPT- and KH550-containing compounds, respectively. At ω = 102 rad s-1, R'(ω,φ) could be empirically described by the Guth equation58 R'(ω,φ)=1+0.67(kφ)+1.62(kφ)2 and the aspect ratio k is estimated as 8.0 and 12.0, respectively, for the TESPT- and KH550-containing compounds. At lower frequencies, the Guth equation fails and R'(ω,φ) might follow scaling laws R'(ω,φ)~φx predicted

by

cluster-cluster

aggregation21

or

fractal

yielding

models.59-60

For

the

KH550-containing compounds, the exponent x varies from 1.1 at ω = 10 rad s-1 to 3.4 at ω = 0.01582 rad s-1 and for the TESPT-containing ones, x is 3.6 at ω = 10-1 rad s-1 and 4.5 at ω = 0.01582 rad s-1, respectively. Theoretically, x is sensitive to the superstructure of nanoparticle flocs and its acceptable theoretical values lie in the range 2.0-5.0 providing that the network elasticity is dominated by that of fractal flocs.61 Experimentally, the found x values lie between 0.2 and 7.2.1,

4, 62

Many attempts being focused on creating a relationship between x and

microscopic interaction meet frustrations because x is sensitive to ω even through the testing is carried at sufficiently small γ,4 as is evidenced for the KH550-containing compounds. Thus different scaling regimes observed previously, for example, in silica/ polyethyleneoxide (x=3.3 at low φ and 26.5 at high φ)63 and smectite/epoxy (x=1.3 at low φ and 7.2 at high φ) systems,64 and the different x values depending on predetermined ω, as observed here and elsewhere,65 do not really reflect the different filler organizations varying with φ.4 Figure 3a-b also shows relative loss modulus, R''(ω,φ)=G''(ω,φ)/G''m(ω), as a function of φ. It is normally that R''(ω,φ) is smaller than R'(ω,φ) at given ω and φ. However, the variation of R''(ω,φ) induced by filling is never clarified in the existing theories. Considering that the polymer and filler play crucial roles in the high- and low-ω regions,2-6 respectively, an attempt is tried to create R'(ω,φ) master curves by normalizing φ with a critical concentration φc defining the hydrodynamic to non-hydrodynamic transition. The created R'(ω,φ) master curves are show in Figure 3c for the TESPT- and KH550-containing compounds with varying φ. Also shown are data of Ref 1 and Ref 2 (φ=0.172). The master curves at φ/φc1 could be described by R'(ω,φ)~φ1.0 and R'(ω,φ)~φ4.2, respectively, and the latter follows 9



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the prediction for nonfluctuating fractal objects.66 The normalization strategy is remarkably revealing because it allows creation of a master curve of R''(ω,φ) without any adjustment along the vertical axis, as shown in Figure 3c. The slopes of the R''(ω,φ) master curves in the hydrodynamic and non-hydrodynamic regimes are smaller than those of R'(ω,φ), being about 0.45 and 2.6, respectively. It is important that the critical concentration φc is dependent on ω, as shown in inset in Figure 3c. In the hydrodynamic regime, φc is sensitive to filler dispersion mediated by the processing technology and the silane introduced in the compounds. On the other hand, in the non-hydrodynamic regime, the differences between φc of the four different compounds are rather small. The finding of time-concentration superpositioning (TCS) principles, i.e., normalizations of both reinforcement and dissipation using a ω-dependent φc, is vital to the understanding of compound’s viscoelasticity. It is helpful for clarifying the longstanding disagreements in the reinforcement studies2-6 and allowing evaluation of the filling-induced variations of dissipation of mechanical energy input in the compounds. The TCS principles reveal that the apparent fluid-to-solid like transition is not a transition dominated by filler structuring usually characterized by a geometrical percolation threshold. On the other hand, dynamics of the bulk phase play a more significant role, which is critical in the hydrodynamic regime. The scaling for nonfluctuating fractal objects works only in the terminal non-hydrodynamic regime where the bulk phase relaxes fully.

10


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105

(b)

TESPT

(a)

104

KH550

0.01582 rad s-1

R', R"

103

0.1

1

102

10

101

100

100 0.02

7

10

0.1

10-1

10-2 -2 10 10-1 100

4.2

KH550 TESPT Ref 1 Ref 2

10 10

ϕ

0.2

(c)

6 5

0.1

0.02

ϕc

108

R', R"

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


101 102 -1

103

2.6

ω (rad s )

104 103

0.45 KH550

102 101

TESPT, Ref 1( ), Ref 2( ) 1.0

0

10

10-1

100

ϕ/ϕc

101

Figure 3. Relative dynamic moduli R' and R'' and their master curves. R' (solid symbols) and R'' (hollow symbols) at five prescribed frequencies as a function of φ for TESPT- (a) and KH550-containing compounds (b) and normalized plot of R' and R'' as a function of φ/φc (c). Legends in (b) are also suitable for both (a) and (c). Also shown in (c) are data of Ref 1 (pentagon) and Ref 2 (hexagon) at φ=0.172. The straight lines in (a) and (b) are drawn according to scaling law for R' and those in (c) are for R' and R''. The inset in (c) shows φc as a function of ω. 11



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Normalization of Linear Rheology in the Hydrodynamic Regime. Besides immobilization of a portion of chains surrounding nanoparticles, filling always retards global diffusion of chains in the bulk phase35-36 and induces a strain amplification effect 67-68 to this dynamically retarded phase. To account for the rheological contributions of the polymer and filler phases, the “two-phase” model2-6, 69-77 following Leonov78 is adopted; to account for the dynamics retardation, terminal relaxation time τc(φ) of the bulk phase in the compounds should be incorporated.72 In the modified “two-phase” model, G*(ω,φ) is formulated as a weighted sum of contributions from the dynamically retarded bulk phase, G*m(ωτc), and the “filler phase”, G*f(ω,φ), i.e., G*(ω,φ) = (1-φ)AfG*m(ωτc) + φG*f(ωτc,φ)

(1)

Here Af(φ) is a strain amplification factor79 defined as the ratio of microscopic strain of interstitial fluid to macroscopically imposed strain of the compounds, which is quoted to explain the reinforcement of filled elastomers67-68 in the high-ω zone80-81 in relation to enlarged polymer contribution.10,

82-83

According to eq 1, plotting reduced complex modulus, Gr*(ω,φ) =

G*(ω,φ)/[(1-φ)Af(φ)], against reduced frequency, ωτc(φ) (Figure 4), should prove the TCS principle in the high-ω zone. A two-step shifting protocol84-85 is applied for creating TCS master curves in this zone. In the first step, the tanδ curve of compounds is normalized by plotting against ωτc(φ); τc(φ=0) for the pure matrix is simply identified as reciprocal of G'm(ω)-G''m(ω) crossover frequency. In the second step, the G'(ω,φ) and G''(ω,φ) curves are vertically shifted by a factor of (1-φ)Af(φ) so as to superpose on those of pure matrix. The superposition is excellent for G'r(ω,φ) and G''r(ω,φ)

in

the

high-ω

zone;

it

is

|ηr*(ω,φ)|/τc(φ)=|η*(ω,φ)|/[(1-φ)Af(φ)τc(φ)],

verified and

by

reduced

reduced

complex

relaxation

time

viscosity, spectra,

Hr(τ)=H(τ)/[(1-φ)Af(φ)] (insets in Figure 4). The TCS principle fails in the low-ω or long-τ zone due to the gradually important influence of the filler phase with increasing φ.

12


106

(a)

(b)

102

10

4

100

100 102

|η*r|/τc (Pa)

τ/τc

101

tanδ

G'r, G''r (Pa)

102

104 107

102

100

105 103 -4 -2 0 10 10 10

106

ωτc

-2

10

10

0

10

2

ωτc

(c)

(d)

-2

10

Hr(τ) (Pa)

100 -4 10

10

-1 10 2 10

0

102 4

10

102 100

104

100

102

|η*r|/τc (Pa)

τ/τc

101

tanδ

G'r, G''r (Pa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Hr(τ) (Pa)

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107

2

10

100 -4 10

100

105 103 -4 -2 0 10 10 10

-2

10

ωτc

0

10

2

10

ωτc

-2

10

0

10

-1 10 2 10

Figure 4. Normalized linear rheology for TESPT- (a and b) and KH550-containing compounds (c and d). G'r (filled symbols: a and c), G''r (hollow symbols: a and c), tanδ (b and d), |ηr*|/τc (insets in a and c) and Hr(τ) as a function of ωτc (insets in b and d). Also shown in (a) and (b) are the data of Ref 1 and Ref 2 for verification of the TCS principle in the high-ω zone. The legends are the same as those in Figure 1.

For clear display the roles of polymer and filler to the reinforcement and filling-induced variation of dissipation, relationship between reduced relative storage modulus of the compounds, R'r(ω,φ)=R'(ω,φ)/[(1-φ)Af(φ)], and relative change of storage modulus of the bulk phase due to retardation, R'm(ω)=G'm(ωτc)/G'm(ω), is examined. Also examined is the relationship 13



between reduced relative loss modulus of the compounds, R''r(ω,φ)=R''(ω,φ)/[(1-φ)Af(φ)], and relative change of loss modulus of the bulk phase due to retardation, R''m(ω)=G''m(ωτc)/G''m(ω). Figure 5 shows the R'r-R'm and R''r-R''m relationships for the compounds. Certainly, the reinforcement and dissipation could be divided into two regimes. In the hydrodynamic regime, both the reinforcement and dissipation are determined by the bulk phase. In the non-hydrodynamic regime, the filler phase contributes greatly to the reinforcement to a degree larger than the dissipation. 105

105 (a)

4

10

104

103

103

(b)

R'r, R"r

R'r, R"r

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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102

102

(2)

(2) 101 0

10 0 10

101

(1)

(1)

0

101

102

10 0 10

R'm, R"m

101

102

R'm, R"m

Figure 5. R'r-R'm (solid symbols) and R''r-R''m relationships (hollow symbols) for TESPT- (a) and KH550-containing compounds (b). Also shown in (a) are the data of Ref 1 and Ref 2 for verification of the TCS principle in the high-ω zone. The Arabic numerals (1), and (2) denote the hydrodynamic and non-hydrodynamic regimes, respectively, for R'r against R'm for the TESPT- and KH550-containing compounds at φ=0.172. The legends are the same as those in Figure 1.

The pure filler effect could be separated according to R'f(ω,φ)=R'(ω,φ)/[(1-φ)Af(φ) R'm(ω)] and R''f(ω,φ)=R''(ω,φ)/[(1-φ)Af(φ)R''m(ω)]. Figure 6 compares the rheological contributions arising from the pure filler effect and the dynamics retardation effect, from which three viscoelastic regimes are distinguished with decreasing ω, i.e., one with both reinforcement and dissipation dominated by polymer [R'f(ω,φ)R'm(ω) and R''f(ω,φ)>R''m(ω]. Note the third one that dominates at low frequencies and high filler loadings. Note also the first one whose contribution 14


Page 15 of 36

is sensitive to filler dispersion, being larger in the KH550-containing compounds than in the TESPT-containing ones.

101

(3) (2)

(1)

100

10

100 0.02

R''f, R''m

1

ω decreasing

(b)

1

(2) (1)

100 0.02

0.1 0.2

ϕ

(3) (2) (1) 0.1

(d)

10

(3)

ω decreasing

100

102

(c)

(3)

ω decreasing

101

R'f, R'm

102

103

(a) ω decreasing

R'f, R'm

103

R''f, R''m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(2) (1)

0.1 0.2

ϕ

Figure 6. Comparison of viscoelastic contributions of the filler (large symbols being the same as those in Figure 1) and polymer phases (small plus-centered symbols with their shapes being the same as those in Figure 1) for TESPT- (a and b) and KH550-containing compounds (c and d). R'f and R'm (a and c) as well as R''f and R''m (b and d) as a function of φ. The Arabic numerals (1), (2) and (3) denote three viscoelastic regimes, i.e., one with reinforcement and dissipation dominated by polymer, another with reinforcement dominated by polymer and dissipation by filler, and a third one with reinforcement and dissipation dominated by filler, with decreasing ω.

Nanoparticles slow down macromolecular diffusion as demonstrated both experimentally and theoretically.35-36, 86-88 To disclose the filling-induced variations in polymer dynamics and the contribution of filler phase, rheological parameters for the compounds and their filler phase are evaluated. Figure 7a-b shows τc(φ) and Af(φ) as a function of φ for the compounds. It is clear that τc(φ) increases with increasing φ and the increment is more marked in the KH550-containing compounds than in others. On the other hand, Af(φ) is almost the same for the different compounds at φ

Reconsideration of the Rheology of Silica Filled Natural Rubber

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