mechanical properties and mullins effect in natural rubber

Research ArticleMechanical Properties and Mullins Effect in Natural RubberReinforced by Grafted Carbon Black

Wen Fu 1 Li Wang 2 Jianning Huang1 Cuiwen Liu1 Wenlong Peng1

Haotuo Xiao1 and Shenglin Li1

1College of Material Science Guangdong University of Petrochemical Technology Maoming Guangdong 525000 China2College of Chemical Engineering Guangdong University of Petrochemical Technology Maoming Guangdong 525000 China

Correspondence should be addressed to Li Wang wanglihaha126com

Received 18 June 2019 Accepted 11 July 2019 Published 1 August 2019

Guest Editor Zhiwei Qiao

Copyright copy 2019 Wen Fu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The obvious polarity difference between the carbon black (CB) and the natural rubber (NR) causes the CB hard to be dispersed inthe NR matrix when the addition amount is large In this paper polyethylene glycol (PEG) was grafted onto the surface of CB bythe liquid phase The grafted carbon black (GCB) was prepared and applied to reinforce NR The main physical and mechanicalproperties of NRwere improved because of the better compatibility betweenGCB andNRTheMullins effect of the vulcanizatewascalculated by the cyclic stress-strain experiment The results showed that the Mullins effect both existed in the virgin NR systemand filled NR system The degree of Mullins effect was increased with the increase of the filler addition but that was different forCB and GCBWhen the filler addition was below 20 phr the Mullins effect of NRGCB was stronger than that of NRCB Howeverwhen the filler addition was over 30 phr the Mullins effect of NRCB was stronger than that of NRGCB The Mullins effect wasaffected by the heat treatment temperature and timeThe mechanisms of the Mullins effect were analyzed

1 Introduction

Because the rubber materials have high elasticity dampingand other excellent properties they have been widely usedin tires electronics military aerospace and other fields [1ndash3] In general the physical and mechanical properties of thepure rubber are not very good so the rubber materials needto be reinforced in order to improve their comprehensiveperformance Carbon black is the main reinforcement agentin the rubber industry [2ndash4] Since CB is a polar material andNR is a nonpolar material the polarity difference between CBand NR is obvious so the dispersion of CB in the NR matrixis difficult when the amount of CB is large thereby causingthe decrease of the physical and mechanical properties ofNR Grafting some polymer chains on the surface of CB toreduce the polarity difference between CB and the matrix isa good strategy thereby enhancing the reinforcing effect ofCB

Chen [5] used the radiation grafting method to graft thepolyethylene (PE) on the surface of carbon blackThe grafting

ratio of PE onto the carbon black surface proceeded and thepercentage of grafting exceeded 90 when the irradiationdose reached 200 kGy Tsubokawa [6] investigated thesurface grafting of hyperbranched poly(amidoamine) ontothe surface by using dendrimer synthesis methodology Thepercentage of poly(amidoamine) grafting reached 962after 10th generation Richner [7] grafted the isocyanateprepolymers on the surface of CB This crosslinked car-bon black was designed as a new active material for elec-trochemical electrodes and the active material for electricdouble-layer capacitor electrodes was produced which hada specific capacitance of up to 200 Fg Yang [8] first syn-thesized the polystyrene poly(styrene-co-maleic anhy-dride) poly[styrene-co-(4-vinylpyridine)] and poly(4-vin-ylpyridine) Then the resultant polymers were grafted ontothe surface of carbon black through a radical trappingreaction It was found that the carbon black grafted withpolystyrene and poly(styrene-co-maleic anhydride) could bedispersed in tetrahydrofuran chloroform dichloromethaneN N-dimethylformamide etc and the carbon black

HindawiAdvances in Polymer TechnologyVolume 2019 Article ID 4523696 11 pageshttpsdoiorg10115520194523696

2 Advances in Polymer Technology

grafted with poly(4-vinylpyridine) and poly[styrene-co-(4-vinylpyridine)] could be well dispersed in ethanol

The required stress at the same certain strain was de-creased after cyclic tension treatment for several times inthe vulcanized rubber composites which was called thestrain softening effect or Mullins effect [9] This effect wasdiscovered by Bouasse and Carriere [10] More followingworks by Mullins pointed out that the Mullins effect notonly existed in the filled rubber system but also in theunfilled rubber system However the Mullins effect of theunfilled rubber system was weaker than that of the filledrubber system [11 12] Other similar researches about theMullins effect had been conducted for example the rubbermatrix (nitrile rubber [13] ethylene propylene diene rubber[14] natural rubber [15] and styrene butadiene rubber[16]) with carbon black [17] silica [18] and other fillers[19]

Some explanatory models were proposed to explain theMullins effect Bueche [20] pointed out that it was a propor-tional relationship between the space change of microparti-cles and the macroscopic deformation With the increase ofthe macroscopic deformation the rubber molecular chainsamong filler particles achieved their ultimate elongation andsome molecular chains would be broken away from thefiller surfaces leading to a decrease of the interaction forcebetween the molecular chains and fillers finally causing theMullins effect Houwink [21] put forward that the Mullinseffect resulted from the slipping of the molecular chainsadsorbed on the filler surface during the stretching processMullins [11] insisted that the filled vulcanized rubber was ahybrid system consisted of the high filler content region (hardphase) and low filler content region (soft phase) During thedeformation process the hard phase would be transferredto the soft phase which led to the Mullins effect This viewwas further perfected by Johnson [22] He pointed out thatthe short molecular chains in the vulcanized rubber systemwould be tangled to form the molecular chain clustersfollowed by the formation of hard phase in the internalSome molecular chains of the hard phase were pulled outand transferred into the soft phase during the deformationprocess Kraus [23] thought that the Mullins effect was thecombination of several effects including the destruction ofthe filler aggregate network and the destruction of the filler-rubber molecular interaction Hamed [24] noted that therubber molecular chains could adsorb on the filler surface toform a rubber shell layer Under the external force the rubbermolecular chains adsorbed on the surface of fillers would bedesorbed thus reducing the thickness of the rubber shell andweakening the interaction between the rubber and carbonblack Roozbeh [12] mentioned that the filled rubber systemcontained two kinds of cross-linking networks themolecularchains cross-linking network of the rubber matrix and theinteraction network of the filler-filler and filler-matrix TheMullins effect was the result of the interaction betweenthese two kinds of cross-linking networks Until now thesemodels are still controversial none of which can provide areasonable and complete explanation for the Mullins effectTable 1 showed the related diagrams of mechanism models ofthe Mullins effect

In this work in order to reduce the polarity differencebetween CB and NR and improve the dispersion of CB inthe NR matrix CB was graft modified with PEG and appliedto reinforce NR The comprehensive performance of NR hasbeen increased with the addition of GCB More importantlythe Mullins effect mechanisms were deduced by comparingthe effects of GCB and CB on the Mullins effect of NR underdifferent conditions

2 Experiments

21 Materials Natural rubber (NR type of 3L) was pur-chased from Guangzhou Beishite Company China Carbonblack (CB type of N330 the average diameter size of 25sim30 nm the specific surface area of 103m2g) was obtainedfromCabot Corporation USA Concentrated nitric acid tol-uene thionyl chloride dibutyl dilaurate zinc oxide (ZnO)stearic acid (SA) and polyethylene glycol (PEG number-average molecular weight of 400) were analytically pure andpurchased from Sigma Aldrich Company USA Poly(12-dihydro-224-trimethyl-quinoline (antioxidant RD) 221015840-dibenzothiazole disulfide (accelerator DM) and sulfur (S)were purchased directly from the market and used asreceived

22 Sample Preparation

221 The Preparation of Grafted Carbon Black 50 g of CBand 350ml of concentrated nitric acid were added to a1000ml three-neck flask the samples were reacted at 60∘Cfor 2 h using the mechanical stirring and then the reactionproduct was filtered washed with deionized water dried at95∘C to obtain the intermediate A 50 g of the intermediateA 125 g of thionyl chloride and 350ml of toluene wereplaced in a 1000ml three-neck flask and the samples werereacted at 0∘C for 30min and then at 120∘C for 30minusing the mechanical stirring The reaction product wasrotary evaporated at 80∘C to remove the unreacted thionylchloride the intermediate B was prepared Subsequently50 g of the intermediate B 25 g of PEG 01ml of dibutyldilaurate and 350ml of toluene were added to a 1000mlthree-neck flask the samples were reacted 0∘C for 30minand then at 120∘C for 1 h using the mechanical stirring Thereaction product was filtered washed with deionized waterdried at 95∘C to obtain the grafted carbon black denoted asGCB

222 The Preparation of NRCB and NRGCB VulcanizatesThe roller gap of two-roll mill was adjusted to about 2mmNR was added and plasticated for 8 minutes and then CB(or GCB) ZnO SA RD DM and S were added to the two-roll mill in turn followed by 5 times side cuts on the left andright and then a triangle package was implemented 7 timesand thin-passing for 8 times Subsequently the compoundswere stored for 24 h and were cured by a press vulcanizer at150∘C for (t90+2) min The mass ratio of NR ZnO SA RDDM and S was 100 5 2 1 1 2 The filler contents were variedfrom 0 to 60 phr

Advances in Polymer Technology 3

Table 1 Schematic diagrams of Mullins effect mechanisms

Models Schematic diagrams

Detachment of themolecular chains [20]

Slippage of themolecular chains [21]

Disentanglement of therubber molecular chains[11 22]

Destruction of the filleraggregates [23]

Rubber shell model [24]

23 Characterization

231 Thermogravimetric Analysis The thermogravimetricanalyzer (TGA 209 F3 Netzsch Germany) was used to testthe graft ratio of PEG on CBThe temperature range was 30sim850∘C the heating ratewas 50 Kmin and the test atmospherewas nitrogen In order to remove the PEG adsorbed on thesurface of CB through physical adsorption GCB was purifiedby reflux condensation for 05 h with toluene and then dried

232 Physical and Mechanical Properties Test The electronictensile testing machine (GT-TCS-2000 Gaotie China) wasused to test the tensile and tear properties The tensilestrength was characterized according to GBT 528-2009 thetensile speed was 200mmmin the thickness was 20mmand the sample shapewas dumbbell-shapedThe tear strength

was tested according to GBT 529-2008 the sample shape wasright angle The Shore A hardness was determined accordingto GBT 531-1999The wear resistance was measured accord-ing to GBT 9867-2008 The apparent crosslink density wastested by the swelling method About 1 g of the vulcanizatewas weighed and cut into small strips about 2mm wideand 1mm thick and the treated samples were stored in acontainer with toluene for 7 d at room temperature Aftercompleting the swelling process these strips were taken outand then the toluene adsorbed on the surface of these stripswas removed using the filter paper subsequently these stripswere weighedThe crosslink density was calculated accordingto the Nory-Rehner formula [25] as follows

V119903 = 1V [ln (1 minus V2) + V2 + 120594V22

V213 minus V22 ] (1)


Mass Change -210

100 200 300 400 500 600

70

75

80

85

90

95

100

Mas

s (

)

CB

GCB

Mass Change -206

Mass Change -2123

Mass Change -092 [1]

[2]

800Temperature (∘C)

Figure 1 TGA analysis of carbon black before and after modification

V119903 is the apparent crosslink density of the vulcanizate V2 isthe volume fraction of the rubber phase in the vulcanizate 120594is the interaction parameters between the rubber and solventv is the molar volume of the solvent

where V2 was calculated according to the formula

V2 = 11989831205881198983120588 + (1198982 minus 1198981) 120588∙ (2)

120588∙ is the density of the solvent 120588 is the density ofthe rubber phase 1198981 is the quality of the vulcanizatebefore swelling 1198982 is the quality of the vulcanizateafter swelling 1198983 is the quality of the rubber phase

233Mullins Effect Test TheMullins effect of the vulcanizatewas calculated by the cyclic stress-strain experiment [26]Thesample was stretched to the specified strain for the first timeand the required energywas recorded asW1 the same samplewas stretched to the same strain for the second time and therequired energy was recorded as W2 Generally speaking thevalue of W2 was less than that of W1 the phenomenon wascalled the strain softening or Mullins effect and the value ofW2W1 was used to represent the degree of theMullins effectIn this work the same sample was stretched to the specifiedstrain at room temperature for the first second third andfourth times and the required energies were recorded as W1W2 W3 and W4 respectively According to some repetitiveexperiments it was found that the value of W4 was similarto that of W3 Hence after the sample was stretched threetimes the Mullins effect was stabilized In order to test theeffect of the treatment temperature and storage time on theMullins effect after the sample was stretched three times thesample was stored for 2 h at 60∘C and then the sample wasstretched to the same specified strain at room temperatureand the required energy was recorded as Ws The Mullinseffects in different cases were calculated using the followingformulas

1198721 = [(1198821 (120576) minus 1198823 (120576)]1198821 (120576) lowast 100 (3)

1198722 = [(1198821 (120576) minus 119882119904 (120576)]1198821 (120576) lowast 100 (4)

1198721 is the degree of the Mullins effect after stretching forthree times at room temperature and1198722 is the degree of theMullins effect after recovery at 60∘C for 2 h

3 Results and Discussion

31The Graft Ratio of PEG on CB Due to the large differencein polarity between CB and NR it is difficult for CB to beuniformly dispersed in the rubber matrix especially whenthe amount of CB is large thereby affecting the physicaland mechanical properties of the rubber The difference inpolarity between CB and NR can be reduced by the graftmodification of CB Hence the dispersibility of CB in therubber matrix is improved significantly so the physical andmechanical properties of the rubber are improved The graftratio of PEGon CBwasmeasured through the TGA curves ofCB and GCB (Figure 1) It can be seen from the figure that themass loss of CB from30∘C to 200∘Cwas 21 Itwas due to theloss of the water adsorbed on the surface of CBThemass lossof CB from 200∘C to 650∘Cwas 092 It was attributed to thecarbonization of the organic components inCBWhile for theGCB sample the mass loss from 200∘C to 650∘C was 2123which was obviously higher than that of CB The reason wasthe PEG was grafted on the surface of CB and it was burneddown during the high temperature process so the graft ratioof PEG on CB could be measured according the TGA curvethe value was about 20

32 Physical and Mechanical Properties of NRCB and NRGCB Figures 2(a)ndash2(f) were the physical and mechanicalproperties of theNRCB andNRGCB composites at differentfiller contents It can be seen from Figures 2(a)ndash2(e) thatwith the increase of the addition amount of CB the tearstrength and shore A hardness were increased gradually theelongation at breakwas decreased gradually and themodulusat 300 and tensile strength of the vulcanizate were firstincreased and then decreased When the CB content was 50phr the modulus at 300 and tensile strength reached thehighest the values were 63 Mpa and 212 Mpa respectivelyHowever when the CB content was increased to 60 phr themodulus at 300 and tensile strength were decreased SinceCB was hard to be dispersed in the rubber matrix whenthe addition amount was large hence the filler 3D network


CB GCB

2

4

6

8

10

Mod

ulus

at 3

00

(MPa

)

10 20 30 40 50 600Filler content (phr)

(a)

CB GCB

5

10

15

20

25

30

Tens

ile st

reng

th (M

pa)


(b)

CB GCB

400

500

600

700

800

Elon

gatio

n at

bre

ak (

)


(c)

CB GCB


20

30

40

50

60

70

80

Tear

stre

ngth

(kN

m)

(d)

CB GCB


30

35

40

45

50

55

60

Shor

e A h

ardn

ess

(e)

CB GCB

02

04

06

08

10

12

14

16

Dru

m ab

rasio

n (g

)

20 30 40 50 6010Filler content (phr)

(f)Figure 2 Physical and mechanical properties of NRCB and NRGCB

structure was formed and the aggregation of fillers occurredthe mechanical properties were affected [27]

For the NRGCB composites with the increase of theaddition amount of GCB the modulus at 300 tensilestrength tear strength and shore A hardness were increasedgradually Unlike theNRCB composites the optimumvaluesof the modulus at 300 tensile strength tear strength andshore A hardness were shown when the addition amount ofGCB was 60 phr In addition the modulus at 300 tensile

strength elongation at break and tear strength of NRGCBwere always bigger than that of NRCB at the same fillercontent Compared with the NRCB composites the increaserates of the modulus at 300 tensile strength elongationat break and tear strength of NRGCB were 556 283338 and 426 respectively when the filler content was50 phr It indicated that the addition of GCB could greatlyimprove the comprehensive physical and mechanical proper-ties of the rubber Since GCB can be better dispersed in the


02

04

06

08

10

12

14

16

18

CB GCB

Cros

slink

den

sity

(10-4

mol

cm

3 )


Figure 3 Apparent crosslink densities of NRCB and NRGCB

rubber matrix it is less likely to form filler aggregation andthe interaction between GCB and NR was stronger therebythe physical and mechanical properties were improved

The wear resistances of NRCB and NRGCB with thedifferent filler content were shown in Figure 2(f) With theincrease of filler content the mass of absolute abrasion wasdecreased gradually which indicated that the addition of CBor GCB was helpful for improving the wear resistance ofNR The wear resistance of NRGCB was better than that ofNRCB when the filler content was the same It is mainlybecause the NRGCB has better dispersibility of the fillerlarger filler-rubber interaction and better tear resistancewhich is beneficial to hinder the generation of cracks andbranch cracks and thus improve the wear resistance [28]

33 Apparent Crosslink Densities of NRCB and NRGCBThe apparent crosslink density is a representation of thedegree of vulcanization including the chemical crosslinks(polysulfidic disulfidic and monosulfidic) as well as thephysical crosslinks (rubber-filler interaction and filler-fillernetwork) [29]The apparent crosslink densities of the NRCBand NRGCB vulcanizates at different filler additions wereshown in Figure 3 It can be seen from the figure that theapparent crosslink density of the virgin NR vulcanizate was067 times 10minus4molcm3 When the amount of the filler was10 phr the apparent crosslink densities of the NRCB andNRGCB vulcanizates were decreased to 030 times 10minus4molcm3and 066 times 10minus4molcm3 respectively This is because theN330 carbon black is alkaline but the accelerator DM isacidic When CB is added to the rubber system DM isadsorbed by CB resulting in a decrease of DM involved inthe crosslinking reaction thereby causing a decrease of thecrosslink density Thereafter the apparent crosslink densitiesof the NRCB and NRGCB vulcanizates were increasedgradually as the amount of filler increased It is due to moreand more rubber-filler interaction and filler-filler networkgeneration with the increase of the filler content [29] Inaddition the apparent crosslink density of NRGCB was

200 strain

CB GCB

10

20

30

40

50

60

Mul

lins e

ffect

()


Figure 4 Effect of filler content on Mullins effect of NRCB andNRGCB

bigger than that of NRCB at the same amount of filler This isbecause GCB has better dispersion in the rubber matrix andthus more filler-rubber interaction was created

34 Effect of Filler Content on Mullins Effect of NRCB andNRGCB The effect of filler content onMullins effect of NRCB and NRGCB composites was shown in Figure 4 It canbe seen from the figure that when the sample was stretchedafter three times at room temperature to make the Mullinseffect stability the degree of Mullins effect of the virgin NRwas 612 It is mainly due to the physical disentanglement ofrubber molecular chains during the stretching process [11]

In addition the degree of Mullins effect was increased asthe increase of filler addition amount whatever CB or GCBwas added to the rubber matrix but the increase rate in theMullins effect of adding CB or GCB was different When thefiller additionwas below 20 phr theMullins effect ofNRGCBwas stronger than that of NRCB This is because when theamount of filler is smaller than 20 phr the filler particlesare only dispersed in the rubber matrix in isolation and theyare unlikely to form a filler-filler 3D network structure [12]The Mullins effect at this time should be resulted from thedisentanglement of rubber molecular chains and destructionof the filler-rubber interaction during the stretching processIn the case of the same amount of rubber matrix the Mullinseffect caused by the disentanglement of rubber molecularchains is similar so the Mullins effect should be mainlycaused by the destruction of the filler-rubber interaction [20]The destruction is mainly achieved by the rubber molecularchainsrsquo shedding and slippage from the surface of fillersThat is the mechanism of the Mullins effect at low fillercontent is due to the molecular chainsrsquo shedding and slippagemechanism The dispersion of GCB in the rubber matrix isimproved compared to CB and the compatibility with therubber matrix is also increased Hence more filler-rubberinteractions are formed on the microscopic level These


200 strain

the value of M1

the value of M2

200 strain

the value of M1

the value of M2

0

10

20

30

40

50

60M

ullin

s effe

ct (

)

10 20 30 40 50 600CB content (phr)

0

5

10

15

20

25

30

35

Mul

lins e

ffect

()

10 20 30 40 50 600GCB content (phr)

Figure 5 Effect of storage on Mullins effect of NRCB and NRGCB

interactions are destroyed during the stretching process thusresulting in greater Mullins effect

However when the filler addition was over 30 phr theMullins effect of NRCB was stronger than that of NRGCBParticularly when the filler addition was 60 phr the degreeof Mullins effect of NRGCB was only 47 of that of NRCBThis is because when the amount of CB is over 30 phr thefiller-filler 3D network structures as a new factor affectingthe Mullins effect began to appear and when the amountof CB reached to 60 phr these filler-filler 3D networkstructures were already intense The filler-filler 3D networkstructure can be destroyed during the stretching processthus leading to obvious Mullins effect [23] Neverthelessfor NRGCB fewer filler-filler 3D network structures weregenerated because GCB has better dispersion in the rubbermatrix so theMullins effect of NRGCB was not serious evenif the amount of filler was large

Moreover when the amount of CB was increased from40 phr to 50 phr the Mullins effect rose sharply from 33to 60 Some authors called this phenomenon a percolationtransition of filler reinforcement [30] At this time variousisolated filler-filler 3D network structures are connected toeach other as a whole This whole is destroyed during thestretching process which leads to a sharp rise in the Mullinseffect However this sudden increase of the Mullins effectdid not occur in NRGCB when the amount of filler wasincreased from 40 phr to 50 phr nor did it occur when theamount of filler was increased from 50 phr to 60 phr It wasalso shown that CB can be dispersedmore uniformly after thegraft modification and it is more difficult to form the filler-filler 3D network structure in the rubber matrix

35 Effect of Storage on Mullins Effect Recovery of NRCBand NRGCB Studying the changes in the Mullins effectduring the storage is helpful for further understanding themechanism of the Mullins effect According to formula (3)and formula (4) the values of1198721 and1198722 of the NRCB andNRGCB samples were calculated and shown in Figures 5(a)

and 5(b) It can be seen from the figure that when no fillerwas added the value of1198722 of the virgin NR vulcanizate wasbigger than that of 1198721 According to the previous analysisthe factor that causes the Mullins effect at this time is only thephysical disentanglement of rubber molecular chains duringthe stretching process So it means that the high temper-ature treatment is good for re-entanglement of the rubbermolecular chains [31] This is because the activity of therubber molecular chains rises thus more re-entanglementsare generated during the high temperature treatment processMore re-entanglements are destroyed during the stretchingprocess and lead to bigger Mullins effect

In addition when the filler content is from 10 phr to60 phr with the increase of the filler content the Mullinseffect was increased gradually during the high temperaturetreatment process But the values of 1198722 of the NRCB andNRGCB samples were smaller than the values of 1198721 oftheir counterparts It indicates that the high temperaturetreatment is beneficial for the regeneration of the filler-rubber interaction and filler-filler 3D network structure [31]However it is only partial regeneration and it is hard toreturn to the initial state of the filler-rubber interaction andfiller-filler 3D network structure so the value of1198722 is alwayssmaller than the value of1198721 at the same filler addition

36 Effect of Storage on Mullins Effect Recovery of NRCBand NRGCB The phenomenological theory is a researchmethod of rubber elasticity theory TheMooney-Rivlin equa-tion is one of the most commonly used expressions in thephenomenological theory [32] which is shown as follows

120590120582 minus 120582minus2 = 211986210 + 211986201 (

1120582) (5)

In formula (5) 120590 is the stress 120590(120582 minus 120582minus2) is defined asthe reduced stress 120582 is the strain along the stress directionand C10 and C01 are constants without clear physical meaning[33]


02 03 04 05 06 07 08 09 1000

05

10

15

20

25

30

abc

CB

I

03 04 05 06 07 08 09 10

03

04

05

06

07

08

09

10

abc

GCB

II(2(

minus1(lowast)))

(2(

minus1(lowast)))

1 1

Figure 6 Mooney curves of NRCB and NRGCB at different conditions

According to the formula (5) the stress-strain curve ofa sample can be transferred to the Mooney-Rivlin curve(hereinafter referred to as Mooney curve) The Mooneycurves of the sample being directly stretched to break thesample being repeatedly stretched to 200 strain for 3 timesand then stretched to break and the sample being repeatedlystretched to 200 strain for 3 times and then placed in anoven at 60∘C for 2 h and then stretched to break were shownin Figure 6 The CB or GCB filler content was 60 phr in thisexperiment According to the formula (5) the ideal Mooneycurve should be a straight line But it can be seen from theFigure 6 that the real Mooney curve was not a straight lineThe reduced stress 120590(120582 minus 120582minus2) first fell and then rose withthe increase of the strain 120582 (look from the right to left ofthe curves) presented a ldquoU-shapedrdquo trend The difference ofthe ideal Mooney curve and real Mooney curve reflects twoadditive effects during the stretching process (1) in the lowstrain region (the right side of the curve) the reduced stressdecrease with the increase of strain is due to theMullins effectof the material (2) In the high strain region (the left side ofthe curve) the reduced stress increases with the increase ofstrain is because of the non-Gaussian behavior of the polymerchains The upturning phenomenon of the reduced stressin high strain region indicates that the polymer chains arestretched to their ultimate elongation [33]

The Mooney curve of the NRCB sample being directlystretched to break (Figure 6(I-a)) showed a very obviousdecline in the low strain region It indicated an obviousMullins effect occurred However when the sample wasrepeatedly stretched to 200 strain for 3 times and thenstretched to break the Mooney curve in the low strain region(Figure 6(I-b)) did not show a significant decline This isbecause the repeated stretching leads to the disentanglementof rubber molecular chains the destruction of the filler-rubber interaction and filler-filler 3D network structurethus leading to the decrease of the Mullins effect Thedestruction of the filler-filler 3D network structure should

be the main cause of the decline of the Mullins effect Whenthe sample was treated in an oven at 60∘C for 2 h afterit has been stretched for 3 times the Mooney curve inthe low strain region (Figure 6(I-c)) presented a relativelysignificant decline compared to Figure 6(I-b) The reason isthat the rubber molecular chains are re-entangled the filler-rubber interaction and filler-filler 3D network structure areregenerated during the high temperature treatment processIn addition Figure 6(I-b) curve was always below Figure 6(I-a) curve and Figure 6(I-c) curve was always above Figure 6(I-b) curve It meant that the stress required for Figure 6(I-b)curve was smaller than that of Figure 6(I-a) curve and thestress required for Figure 6(I-c) curve was bigger than thatof Figure 6(I-b) curve at the same strain It also indicatesthat the repeated stretching leads to the disentanglement ofrubber molecular chains the destruction of the filler-rubberinteraction and filler-filler 3D network structure the hightemperature treatment is helpful for the re-entanglement ofrubber molecular chains and the regeneration of the filler-rubber interaction and filler-filler 3D network structure

The trend of the Mooney curves of the NRGCB samplesunder the three different stretching conditions (Figure 6(I-ab c)) was similar to that of the NRCB samples (Figure 6(II-a b c)) but there were some differences that had to bementioned First when 120582minus1 was changed from 10 to 09the value of 1205902(120582 minus 120582minus2) of NRCB was changed from 272to 098 However the value of 1205902(120582 minus 120582minus2) of NRGCBwas changed from 086 to 076 which was obviously smallerthan that of NRCB This also showed that the Mullinseffect of NRGCB was lower when the filler content was60 phr Second whatever being directly stretched to break(Figure 6(II-a)) being repeatedly stretched to 200 strainfor 3 times and then stretched to break (Figure 6(II-b)) andbeing repeatedly stretched to 200 strain for 3 times and thenplaced in an oven at 60∘C for 2 h and then stretched to break(Figure 6(II-c)) the Mooney curves of the samples in the lowstrain region all presented a relatively significant decline It


= Chemical bonding pointof filler-rubber interaction

Permanent crosslink network Stretch deformation of permanent crosslink network

Chains physical entanglement Chains disentanglement

Filler-rubber interaction Filler-rubber interaction broken

Filler-filler 3D network Filler-filler 3D network broken

= filler particle

= filler particle

polymerfiller vulcanizate

= Polymer chain

= Physical bonding pointof filler-rubber interaction

Figure 7 Filler reinforcement and Mullins effect mechanisms

illustrates that the reason causing theMullins effect of NRCBand the Mullins effect of NRGCB is different The mainreason causing the Mullins effect of NRCB is the destructionof the filler-filler 3Dnetwork structure while themain reasoncausing theMullins effect ofNRGCB is the destruction of thefiller-rubber interaction

37 Filler Reinforcement and Mullins Effect MechanismsCombining the previous analyses and drawing on Roozbehrsquosviewpoint [12] the polymerfiller vulcanizate system can bedivided into four parts the permanent crosslink networkof polymer chains crosslinked by the vulcanizing agents(Figure 7 row 1) the physical entanglement network of poly-mer chains (Figure 7 row 2) the filler-rubber interactionsystem (Figure 7 row 3) and the filler-filler 3D networksystem (Figure 7 row 4) The combined action of thesefour parts constitutes the reinforcing mechanisms of poly-merfiller vulcanizate system and the Mullins effect mech-anisms are also caused by the changes of these four partsat different situations The filler reinforcement and Mullinseffect mechanisms are analyzed as follows

(1) For the virgin polymer vulcanizate system with nofiller the strength of the vulcanizate is derived from theorientation and fracture of the polymer permanent crosslinknetwork and the crystallization owing to the orientationof the polymer chains during the stretching process [34]While the Mullins effect should be mainly attributed to thedisentanglement of the polymer chains during the stretchingprocess (Figure 7 row 2) and theMullins effect caused by thisdisentanglement is weak

(2) For the polymer vulcanizate system with low fillercontent the orientation and fracture of the polymer per-manent crosslink network and the crystallization can resultin the strength improvement the filler-rubber interactionis another factor to lead to the strength improvement ofthe vulcanizate The external force acting on the rubbermatrix is transferred to the rigid filler through the filler-rubber bonding points so the strength of the vulcanizateis improved The filler-rubber bonding points are includingthe filler-rubber physical bonding points connected throughthe noncovalent bonds and filler-rubber chemical bondingpoints connected through the covalent bonds The Mullins


effect should be mainly attributed to the destruction of thefiller-rubber physical bonding points and chemical bondingpoints and the slippage of the polymer chains on the surfaceof the fillers (Figure 7 row 3) Under the same filler contentthe better the dispersion of the filler in the rubber matrix andthe better the compatibility with the rubber matrix exhibitthe more filler-rubber interaction points are formed Themore filler-rubber interaction points are destroyed during thestretching process the more obvious Mullins effect This iswhy the Mullins effect of NRGCB is stronger than that ofNRCB when the filler is below 20 phr

(3) For the polymer vulcanizate system with high fillercontent the more filler-rubber interaction points are formedbecause of the bigger filler content thus the strength isimproved But when the addition amount of the filler is toobig the filler-filler 3D network structure will be formed inthe rubber matrix thus causing the filler agglomeration Theagglomeration of the filler in the rubber matrix causes thestress concentration thereby resulting in a decrease in thetensile strength This is why the tensile strength of the rubberis lowered when the amount of CB is increased from 50 phrto 60 phr The Mullins effect at this time should be mainlyascribed to the destruction of the filler-filler 3D networkstructure during the stretching process (Figure 7 row 4)TheMullins effect resulted from the destruction of the filler-filler3D network being greater than that caused by the destruc-tion of the filler-rubber interaction It can be seen fromFigure 4

4 Conclusions

(1) About 20 polyethylene glycol of the total mass wasgrafted on the surface of the carbon black thus the dispersionof the carbonblack in the rubbermatrix and the compatibilitywith the rubber matrix were improved thereby the compre-hensive performance being increased

(2) The degree of Mullins effect was increased with theincrease of filler However when the filler addition wasbelow 20 phr the Mullins effect of NRGCB was strongerthan that of NRCB When the filler addition was over 30phr the Mullins effect of NRCB was stronger than thatof NRGCB The degree of Mullins effect of NRGCB wasonly 47 of that of NRCB when the filler addition was60 phr The Mullins effect was increased gradually duringthe high temperature treatment process because of the re-entanglement of the rubbermolecular chains regeneration ofthe filler-rubber interaction and filler-filler 3D network struc-ture

(3) For the virgin polymer vulcanizate system with nofiller the Mullins effect should be mainly attributed to thedisentanglement of the polymer chains during the stretchingprocess For the polymer vulcanizate system with low fillercontent the Mullins effect should be mainly ascribed tothe destruction of the filler-rubber interaction during thestretching process For the polymer vulcanizate system withhigh filler content the Mullins effect at this time should bemainly resulted from the destruction of the filler-filler 3Dnetwork structure during the stretching process

Data Availability

The data used to support the findings of this study areincluded within the article

Conflicts of Interest

The authors declare that they have no conflicts of interestregarding the publication of this paper

Acknowledgments

This work was supported by the Natural ScienceFoundation of Guangdong Province (2017A0303106632018A030307018 and 2018A0303070003) the Foundation ofGuangdong Province RubberPlastic Materials Preparationamp Processing Engineering Technology Development Centre(2015B090903083) Distinguished Young Talents in HigherEducation of Guangdong (517053) Maoming Science andTechnology Project (517055) and Guangdong ResearchCenter for Unconventional Energy Engineering Technology(GF2018A005)

References

[1] X Fan H Xu Q Zhang D Xiao Y Song and Q ZhengldquoInsight into the weak strain overshoot of carbon black fillednatural rubberrdquo Polymer Journal vol 167 pp 109ndash117 2019

[2] P Yuvaraj J R Rao N N Fathima N Natchimuthu andR Mohan ldquoComplete replacement of carbon black filler inrubber sole with CaO embedded activated carbon derived fromtannery solid wasterdquo Journal of Cleaner Production vol 170 pp446ndash450 2018

[3] B Sripornsawat S Saiwari and C Nakason ldquoThermoplasticvulcanizates based on waste truck tire rubber and copolyesterblends reinforced with carbon blackrdquo Waste Management vol79 pp 638ndash646 2018

[4] X Du Y Zhang X Pan F Meng J You and Z Wang ldquoPrepa-ration and properties of modified porous starchcarbon blacknatural rubber compositesrdquoComposites Part B Engineering vol156 pp 1ndash7 2019

[5] J ChenYMaekawaMYoshida andNTsubokawa ldquoRadiationgrafting of polyethylene onto conductive carbon black andapplication as a novel gas sensorrdquo Polymer Journal vol 34 no1 pp 30ndash35 2002

[6] N Tsubokawa T Satoh M Murota S Sato and H ShimizuldquoGrafting of hyperbranched poly(amidoamine) onto carbonblack surfaces using dendrimer synthesis methodologyrdquo Poly-mers for Advanced Technologies vol 12 no 10 pp 596ndash6022001

[7] R Richner S Muller and AWokaun ldquoGrafted and crosslinkedcarbon black as an electrode material for double layer capaci-torsrdquo Carbon vol 40 no 3 pp 307ndash314 2002

[8] Q Yang L Wang W Xiang J Zhou and J Li ldquoGrafting poly-mers onto carbon black surface by trapping polymer radicalsrdquoPolymer Journal vol 48 no 10 pp 2866ndash2873 2007

[9] D Julie F Bruno andG Pierre ldquoA reviewon theMullins effectrdquoEuropean Polymer Journal vol 45 no 3 pp 601ndash612 2009

[10] H Bouasse and Z Carriere ldquoSur les courbes de traction ducaoutchouc vulcanizerdquo Annales de la faculte des sciences deToulouse vol 5 no 3 pp 257ndash283 1903


[11] L Mullins ldquoEffect of stretching on the properties of rubberrdquoRubber Chemistry and Technology vol 21 no 2 pp 281ndash3001948

[12] R Dargazany and M Itskov ldquoA network evolution model forthe anisotropic Mullins effect in carbon black filled rubbersrdquoInternational Journal of Solids and Structures vol 46 no 16 pp2967ndash2977 2009

[13] E B da Rocha F N Linhares C F Gabriel AM de Sousa andC R Furtado ldquoStress relaxation of nitrile rubber compositesfilled with a hybrid metakaolincarbon black filler under tensileand compressive forcesrdquo Applied Clay Science vol 151 pp 181ndash188 2018

[14] Q Liu K Zhang X Zhang and Z Wang ldquoStrengthen-ing effect of mullins effect of high- density polyethyleneethylenendashpropylenendashdiene terpolymer thermoplastic vulcan-izates under compression moderdquo Journal of ThermoplasticComposite Materials vol 31 no 10 pp 1310ndash1322 2017

[15] A Ivanoska-Dacikj G Bogoeva-Gaceva S Rooj S Wieszlignerand G Heinrich ldquoFine tuning of the dynamic mechanicalproperties of natural rubbercarbon nanotube nanocompositesby organically modified montmorillonite a first step in obtain-ing high-performance damping material suitable for seismicapplicationrdquo Applied Clay Science vol 118 pp 99ndash106 2015

[16] J Diani M Brieu and P Gilormini ldquoEffect of filler content andcrosslink density on the mechanical properties of carbon-blackfilled SBRsrdquo in Proceedings of the 10th European Conferenceon Constitutive Models for Rubber ECCMR X 2017 pp 3ndash10Balkema August 2017

[17] C Matthew and S A D F Davide ldquoReversibility of the Mullinseffect for extending the life of rubber componentsrdquo PlasticsRubber and Composites vol 5 pp 24ndash31 2018

[18] R Yang Y Song and Q Zheng ldquoPayne effect of silica-filledstyrene-butadiene rubberrdquo Polymer Journal vol 116 pp 304ndash313 2017

[19] S K Srivastava and Y K Mishra ldquoNanocarbon reinforcedrubber nanocomposites Detailed insights about mechanicaldynamical mechanical properties payne and mullin effectsrdquoNanomaterials vol 8 no 11 pp 945ndash3021 2018

[20] F Bueche ldquoMolecular basis for the mullins effectrdquo Journal ofApplied Polymer Science vol 4 no 10 pp 107ndash114

[21] R Houwink ldquoSlipping of molecules during the deformation ofreinforced rubberrdquo Rubber Chemistry and Technology vol 29no 3 pp 888ndash893 1956

[22] M A Johnson and M F Beatty ldquoA constitutive equationfor the Mullins effect in stress controlled uniaxial extensionexperimentsrdquo ContinuumMechanics andThermodynamics vol5 no 4 pp 301ndash318 1993

[23] G Kraus CW Childers and KW Rollmann ldquoStress softeningin carbon black reinforced vulcanizates strain rate and temper-ature effectsrdquo Rubber Chemistry and Technology vol 39 no 5pp 1530ndash1543 1966

[24] G R Hamed and S Hatfield ldquoOn the role of bound rubberin carbon-black reinforcementrdquoRubber Chemistry and Technol-ogy vol 62 no 1 pp 143ndash156 1989

[25] T A Vilgis J Sommer and G Heinrich ldquoSwelling and fractalheterogeneities in networksrdquoMacromolecular Symposia vol 93no 1 pp 205ndash212 1995

[26] M Cheng and W Chen ldquoExperimental investigation of thestressndashstretch behavior of EPDM rubber with loading rateeffectsrdquo International Journal of Solids and Structures vol 40no 18 pp 4749ndash4768 2003

[27] J Frohlich W Niedermeier and H-D Luginsland ldquoThe effectof filler-filler and filler-elastomer interaction on rubber rein-forcementrdquo Composites Part A Applied Science and Manufac-turing vol 36 no 4 pp 449ndash460 2005

[28] H H Hassan E Ateia N A Darwish S F Halim and AK Abd El-Aziz ldquoEffect of filler concentration on the physico-mechanical properties of super abrasion furnace black and silicaloaded styrene butadiene rubberrdquoMaterials and Corrosion vol34 pp 533ndash540 2012

[29] J J Brennan and D H Lambert ldquoRubbermdashblack interactioninfluence on cure level of vulcanizatesrdquo Rubber Chemistry andTechnology vol 45 no 1 pp 94ndash105 1972

[30] J Zhou Y Song Q Zheng Q Wu andM Zhang ldquoPercolationtransition and hydrostatic piezoresistance for carbon blackfilled poly(methylvinylsilioxane) vulcanizatesrdquo Carbon vol 46no 4 pp 679ndash691 2008

[31] G BohmW TomaszewskiW Cole and T Hogan ldquoFurtheringthe understanding of the non linear response of filler reinforcedelastomersrdquoPolymer Journal vol 51 no 9 pp 2057ndash2068 2010

[32] N Kumar and V V Rao ldquoHyperelastic Mooney-Rivlin modeldetermination and physical interpretation of material con-stantsrdquo International Journal of Mechanical Engineering vol 6no 1 pp 43ndash46 2016

[33] W Fu and LWang ldquoResearch on Payne effect of natural rubberreinforced by graft-modified silicardquo Journal of Applied Polymervol 133 no 36 pp 43891ndash43898 2016

[34] J Chenal C Gauthier L Chazeau L Guy and Y BomalldquoParameters governing strain induced crystallization in fillednatural rubberrdquo Polymer Journal vol 48 no 23 pp 6893ndash69012007

CorrosionInternational Journal of

Hindawiwwwhindawicom Volume 2018

Advances in

Materials Science and EngineeringHindawiwwwhindawicom Volume 2018


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Chemistry

Analytical ChemistryInternational Journal of


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Polymer ScienceInternational Journal of



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Journal ofEngineeringVolume 2018

Applied ChemistryJournal of


NanotechnologyHindawiwwwhindawicom Volume 2018

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High Energy PhysicsAdvances in

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

TribologyAdvances in



ChemistryAdvances in


Advances inPhysical Chemistry


BioMed Research InternationalMaterials

Journal of


Na

nom

ate

ria

ls


Journal ofNanomaterials

Submit your manuscripts atwwwhindawicom


grafted with poly(4-vinylpyridine) and poly[styrene-co-(4-vinylpyridine)] could be well dispersed in ethanol

The required stress at the same certain strain was de-creased after cyclic tension treatment for several times inthe vulcanized rubber composites which was called thestrain softening effect or Mullins effect [9] This effect wasdiscovered by Bouasse and Carriere [10] More followingworks by Mullins pointed out that the Mullins effect notonly existed in the filled rubber system but also in theunfilled rubber system However the Mullins effect of theunfilled rubber system was weaker than that of the filledrubber system [11 12] Other similar researches about theMullins effect had been conducted for example the rubbermatrix (nitrile rubber [13] ethylene propylene diene rubber[14] natural rubber [15] and styrene butadiene rubber[16]) with carbon black [17] silica [18] and other fillers[19]

Some explanatory models were proposed to explain theMullins effect Bueche [20] pointed out that it was a propor-tional relationship between the space change of microparti-cles and the macroscopic deformation With the increase ofthe macroscopic deformation the rubber molecular chainsamong filler particles achieved their ultimate elongation andsome molecular chains would be broken away from thefiller surfaces leading to a decrease of the interaction forcebetween the molecular chains and fillers finally causing theMullins effect Houwink [21] put forward that the Mullinseffect resulted from the slipping of the molecular chainsadsorbed on the filler surface during the stretching processMullins [11] insisted that the filled vulcanized rubber was ahybrid system consisted of the high filler content region (hardphase) and low filler content region (soft phase) During thedeformation process the hard phase would be transferredto the soft phase which led to the Mullins effect This viewwas further perfected by Johnson [22] He pointed out thatthe short molecular chains in the vulcanized rubber systemwould be tangled to form the molecular chain clustersfollowed by the formation of hard phase in the internalSome molecular chains of the hard phase were pulled outand transferred into the soft phase during the deformationprocess Kraus [23] thought that the Mullins effect was thecombination of several effects including the destruction ofthe filler aggregate network and the destruction of the filler-rubber molecular interaction Hamed [24] noted that therubber molecular chains could adsorb on the filler surface toform a rubber shell layer Under the external force the rubbermolecular chains adsorbed on the surface of fillers would bedesorbed thus reducing the thickness of the rubber shell andweakening the interaction between the rubber and carbonblack Roozbeh [12] mentioned that the filled rubber systemcontained two kinds of cross-linking networks themolecularchains cross-linking network of the rubber matrix and theinteraction network of the filler-filler and filler-matrix TheMullins effect was the result of the interaction betweenthese two kinds of cross-linking networks Until now thesemodels are still controversial none of which can provide areasonable and complete explanation for the Mullins effectTable 1 showed the related diagrams of mechanism models ofthe Mullins effect

In this work in order to reduce the polarity differencebetween CB and NR and improve the dispersion of CB inthe NR matrix CB was graft modified with PEG and appliedto reinforce NR The comprehensive performance of NR hasbeen increased with the addition of GCB More importantlythe Mullins effect mechanisms were deduced by comparingthe effects of GCB and CB on the Mullins effect of NR underdifferent conditions

2 Experiments

21 Materials Natural rubber (NR type of 3L) was pur-chased from Guangzhou Beishite Company China Carbonblack (CB type of N330 the average diameter size of 25sim30 nm the specific surface area of 103m2g) was obtainedfromCabot Corporation USA Concentrated nitric acid tol-uene thionyl chloride dibutyl dilaurate zinc oxide (ZnO)stearic acid (SA) and polyethylene glycol (PEG number-average molecular weight of 400) were analytically pure andpurchased from Sigma Aldrich Company USA Poly(12-dihydro-224-trimethyl-quinoline (antioxidant RD) 221015840-dibenzothiazole disulfide (accelerator DM) and sulfur (S)were purchased directly from the market and used asreceived

22 Sample Preparation

221 The Preparation of Grafted Carbon Black 50 g of CBand 350ml of concentrated nitric acid were added to a1000ml three-neck flask the samples were reacted at 60∘Cfor 2 h using the mechanical stirring and then the reactionproduct was filtered washed with deionized water dried at95∘C to obtain the intermediate A 50 g of the intermediateA 125 g of thionyl chloride and 350ml of toluene wereplaced in a 1000ml three-neck flask and the samples werereacted at 0∘C for 30min and then at 120∘C for 30minusing the mechanical stirring The reaction product wasrotary evaporated at 80∘C to remove the unreacted thionylchloride the intermediate B was prepared Subsequently50 g of the intermediate B 25 g of PEG 01ml of dibutyldilaurate and 350ml of toluene were added to a 1000mlthree-neck flask the samples were reacted 0∘C for 30minand then at 120∘C for 1 h using the mechanical stirring Thereaction product was filtered washed with deionized waterdried at 95∘C to obtain the grafted carbon black denoted asGCB

222 The Preparation of NRCB and NRGCB VulcanizatesThe roller gap of two-roll mill was adjusted to about 2mmNR was added and plasticated for 8 minutes and then CB(or GCB) ZnO SA RD DM and S were added to the two-roll mill in turn followed by 5 times side cuts on the left andright and then a triangle package was implemented 7 timesand thin-passing for 8 times Subsequently the compoundswere stored for 24 h and were cured by a press vulcanizer at150∘C for (t90+2) min The mass ratio of NR ZnO SA RDDM and S was 100 5 2 1 1 2 The filler contents were variedfrom 0 to 60 phr









23 Characterization




V119903 = 1V [ln (1 minus V2) + V2 + 120594V22

V213 minus V22 ] (1)


Mass Change -210

100 200 300 400 500 600

70

75

80

85

90

95

100

Mas

s (

)

CB

GCB

Mass Change -206

Mass Change -2123


[2]





V2 = 11989831205881198983120588 + (1198982 minus 1198981) 120588∙ (2)



1198721 = [(1198821 (120576) minus 1198823 (120576)]1198821 (120576) lowast 100 (3)

1198722 = [(1198821 (120576) minus 119882119904 (120576)]1198821 (120576) lowast 100 (4)






CB GCB

2

4

6

8

10

Mod

ulus

at 3

00

(MPa

)


(a)

CB GCB

5

10

15

20

25

30

Tens

ile st

reng

th (M

pa)


(b)

CB GCB

400

500

600

700

800

Elon

gatio

n at

bre

ak (

)


(c)

CB GCB


20

30

40

50

60

70

80

Tear

stre

ngth

(kN

m)

(d)

CB GCB


30

35

40

45

50

55

60

Shor

e A h

ardn

ess

(e)

CB GCB

02

04

06

08

10

12

14

16

Dru

m ab

rasio

n (g

)







02

04

06

08

10

12

14

16

18

CB GCB

Cros

slink

den

sity

(10-4

mol

cm

3 )






200 strain

CB GCB

10

20

30

40

50

60

Mul

lins e

ffect

()







200 strain

the value of M1

the value of M2

200 strain

the value of M1

the value of M2

0

10

20

30

40

50

60M

ullin

s effe

ct (

)

10 20 30 40 50 600CB content (phr)

0

5

10

15

20

25

30

35

Mul

lins e

ffect

()

10 20 30 40 50 600GCB content (phr)









120590120582 minus 120582minus2 = 211986210 + 211986201 (

1120582) (5)



02 03 04 05 06 07 08 09 1000

05

10

15

20

25

30

abc

CB

I

03 04 05 06 07 08 09 10

03

04

05

06

07

08

09

10

abc

GCB

II(2(

minus1(lowast)))

(2(

minus1(lowast)))

1 1












= filler particle

= filler particle


= Polymer chain










4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls












23 Characterization




V119903 = 1V [ln (1 minus V2) + V2 + 120594V22

V213 minus V22 ] (1)


Mass Change -210

100 200 300 400 500 600

70

75

80

85

90

95

100

Mas

s (

)

CB

GCB

Mass Change -206

Mass Change -2123


[2]





V2 = 11989831205881198983120588 + (1198982 minus 1198981) 120588∙ (2)



1198721 = [(1198821 (120576) minus 1198823 (120576)]1198821 (120576) lowast 100 (3)

1198722 = [(1198821 (120576) minus 119882119904 (120576)]1198821 (120576) lowast 100 (4)






CB GCB

2

4

6

8

10

Mod

ulus

at 3

00

(MPa

)


(a)

CB GCB

5

10

15

20

25

30

Tens

ile st

reng

th (M

pa)


(b)

CB GCB

400

500

600

700

800

Elon

gatio

n at

bre

ak (

)


(c)

CB GCB


20

30

40

50

60

70

80

Tear

stre

ngth

(kN

m)

(d)

CB GCB


30

35

40

45

50

55

60

Shor

e A h

ardn

ess

(e)

CB GCB

02

04

06

08

10

12

14

16

Dru

m ab

rasio

n (g

)







02

04

06

08

10

12

14

16

18

CB GCB

Cros

slink

den

sity

(10-4

mol

cm

3 )






200 strain

CB GCB

10

20

30

40

50

60

Mul

lins e

ffect

()







200 strain

the value of M1

the value of M2

200 strain

the value of M1

the value of M2

0

10

20

30

40

50

60M

ullin

s effe

ct (

)

10 20 30 40 50 600CB content (phr)

0

5

10

15

20

25

30

35

Mul

lins e

ffect

()

10 20 30 40 50 600GCB content (phr)









120590120582 minus 120582minus2 = 211986210 + 211986201 (

1120582) (5)



02 03 04 05 06 07 08 09 1000

05

10

15

20

25

30

abc

CB

I

03 04 05 06 07 08 09 10

03

04

05

06

07

08

09

10

abc

GCB

II(2(

minus1(lowast)))

(2(

minus1(lowast)))

1 1












= filler particle

= filler particle


= Polymer chain










4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





Mass Change -210

100 200 300 400 500 600

70

75

80

85

90

95

100

Mas

s (

)

CB

GCB

Mass Change -206

Mass Change -2123


[2]





V2 = 11989831205881198983120588 + (1198982 minus 1198981) 120588∙ (2)



1198721 = [(1198821 (120576) minus 1198823 (120576)]1198821 (120576) lowast 100 (3)

1198722 = [(1198821 (120576) minus 119882119904 (120576)]1198821 (120576) lowast 100 (4)






CB GCB

2

4

6

8

10

Mod

ulus

at 3

00

(MPa

)


(a)

CB GCB

5

10

15

20

25

30

Tens

ile st

reng

th (M

pa)


(b)

CB GCB

400

500

600

700

800

Elon

gatio

n at

bre

ak (

)


(c)

CB GCB


20

30

40

50

60

70

80

Tear

stre

ngth

(kN

m)

(d)

CB GCB


30

35

40

45

50

55

60

Shor

e A h

ardn

ess

(e)

CB GCB

02

04

06

08

10

12

14

16

Dru

m ab

rasio

n (g

)







02

04

06

08

10

12

14

16

18

CB GCB

Cros

slink

den

sity

(10-4

mol

cm

3 )






200 strain

CB GCB

10

20

30

40

50

60

Mul

lins e

ffect

()







200 strain

the value of M1

the value of M2

200 strain

the value of M1

the value of M2

0

10

20

30

40

50

60M

ullin

s effe

ct (

)

10 20 30 40 50 600CB content (phr)

0

5

10

15

20

25

30

35

Mul

lins e

ffect

()

10 20 30 40 50 600GCB content (phr)









120590120582 minus 120582minus2 = 211986210 + 211986201 (

1120582) (5)



02 03 04 05 06 07 08 09 1000

05

10

15

20

25

30

abc

CB

I

03 04 05 06 07 08 09 10

03

04

05

06

07

08

09

10

abc

GCB

II(2(

minus1(lowast)))

(2(

minus1(lowast)))

1 1












= filler particle

= filler particle


= Polymer chain










4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





CB GCB

2

4

6

8

10

Mod

ulus

at 3

00

(MPa

)


(a)

CB GCB

5

10

15

20

25

30

Tens

ile st

reng

th (M

pa)


(b)

CB GCB

400

500

600

700

800

Elon

gatio

n at

bre

ak (

)


(c)

CB GCB


20

30

40

50

60

70

80

Tear

stre

ngth

(kN

m)

(d)

CB GCB


30

35

40

45

50

55

60

Shor

e A h

ardn

ess

(e)

CB GCB

02

04

06

08

10

12

14

16

Dru

m ab

rasio

n (g

)







02

04

06

08

10

12

14

16

18

CB GCB

Cros

slink

den

sity

(10-4

mol

cm

3 )






200 strain

CB GCB

10

20

30

40

50

60

Mul

lins e

ffect

()







200 strain

the value of M1

the value of M2

200 strain

the value of M1

the value of M2

0

10

20

30

40

50

60M

ullin

s effe

ct (

)

10 20 30 40 50 600CB content (phr)

0

5

10

15

20

25

30

35

Mul

lins e

ffect

()

10 20 30 40 50 600GCB content (phr)









120590120582 minus 120582minus2 = 211986210 + 211986201 (

1120582) (5)



02 03 04 05 06 07 08 09 1000

05

10

15

20

25

30

abc

CB

I

03 04 05 06 07 08 09 10

03

04

05

06

07

08

09

10

abc

GCB

II(2(

minus1(lowast)))

(2(

minus1(lowast)))

1 1












= filler particle

= filler particle


= Polymer chain










4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





02

04

06

08

10

12

14

16

18

CB GCB

Cros

slink

den

sity

(10-4

mol

cm

3 )






200 strain

CB GCB

10

20

30

40

50

60

Mul

lins e

ffect

()







200 strain

the value of M1

the value of M2

200 strain

the value of M1

the value of M2

0

10

20

30

40

50

60M

ullin

s effe

ct (

)

10 20 30 40 50 600CB content (phr)

0

5

10

15

20

25

30

35

Mul

lins e

ffect

()

10 20 30 40 50 600GCB content (phr)









120590120582 minus 120582minus2 = 211986210 + 211986201 (

1120582) (5)



02 03 04 05 06 07 08 09 1000

05

10

15

20

25

30

abc

CB

I

03 04 05 06 07 08 09 10

03

04

05

06

07

08

09

10

abc

GCB

II(2(

minus1(lowast)))

(2(

minus1(lowast)))

1 1












= filler particle

= filler particle


= Polymer chain










4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





200 strain

the value of M1

the value of M2

200 strain

the value of M1

the value of M2

0

10

20

30

40

50

60M

ullin

s effe

ct (

)

10 20 30 40 50 600CB content (phr)

0

5

10

15

20

25

30

35

Mul

lins e

ffect

()

10 20 30 40 50 600GCB content (phr)









120590120582 minus 120582minus2 = 211986210 + 211986201 (

1120582) (5)



02 03 04 05 06 07 08 09 1000

05

10

15

20

25

30

abc

CB

I

03 04 05 06 07 08 09 10

03

04

05

06

07

08

09

10

abc

GCB

II(2(

minus1(lowast)))

(2(

minus1(lowast)))

1 1












= filler particle

= filler particle


= Polymer chain










4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls





02 03 04 05 06 07 08 09 1000

05

10

15

20

25

30

abc

CB

I

03 04 05 06 07 08 09 10

03

04

05

06

07

08

09

10

abc

GCB

II(2(

minus1(lowast)))

(2(

minus1(lowast)))

1 1












= filler particle

= filler particle


= Polymer chain










4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls










= filler particle

= filler particle


= Polymer chain










4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls







4 Conclusions




Data Availability




Acknowledgments


References






































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls































Advances in



Journal of

Chemistry















Journal of





Volume 2018









Journal of


Na

nom

ate

ria

ls




mechanical properties and mullins effect in natural rubber

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