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2 Temperature-induced crystallization (TIC) and strain-induced crystallization (SIC)

2 Temperature-induced crystallization (TIC) and strain-induced crystallization (SIC)

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The effect of SIC on the physical properties of NR



137



diffraction (WAXD) studies have confirmed the presence of crystals in cold

crystallizing un-vulcanized NR, although the microstructure of crystals – as

may be determined by small angle X-ray scattering (SAXS) – has not yet

been reported. Therefore, un-vulcanized NR creates crystals without a certain

order of lamellar structure under static conditions at low temperatures.

SIC has been observed at high temperatures (75°C and 100°C) (Flory,

1947; Toki et al., 2005). Flory found SIC occuring with a rise in melting

temperature (Tm), attributing this rise to decreased entropy due to deformation

(Flory, 1947; Yamamoto and White, 1971; Tosaka, 2009); this in turn

suggests that higher deformation induces higher Tm of SIC. SIC takes place

over a duration of 60–100 nanoseconds (Mitchell and Meier, 1968; Tosaka

et al., 2006), in contrast to the several hours required for TIC. At the high

altitudes of intercontinental flight, airplane tires are exposed to temperatures

of –50°C and low air pressure for more than six hours. In such cases, NR will

crystallize, but not by TIC; NR compounds might be vulcanized with more

than 2 phr of sulfur, a few phr of stearic acid, a few phr of anti-oxidants,

and about 40 phr of carbon black, all of which hinder TIC. Vital parts of

the tire – especially the fiber cord coating rubber – may already undergo

strain when the tire is formed and vulcanized; at higher altitudes, where air

pressure inside of the tire is high and the air pressure on the outside reduces

significantly, the tire would be expanded by air pressure, increasing strain on

the coating gum. NR compounds in an airplane tire might thus be crystallized

by SIC. The comparison of TIC and SIC on crystal structure and crystallites

is discussed (Che et al., 2013b).



5.3



Stress relaxation and SIC



When vulcanized NR is stretched and fixed at certain extension, it shows

stress relaxation. The stress relaxation of vulcanized rubber has been studied

extensively with reference to birefringence (Treloar, 1941), dilatometry

(Gent, 1954a), and X-ray diffraction (Toki et al., 2005; Rault et al., 2006).

The saturation values of birefringence of vulcanized NR at fixed strain are

approximately proportional to the changes in density by different extensions

at 0°C, suggesting that the orientation and crystallization of rubber chains

occur in deformed state (Treloar, 1941). The stress in deformed vulcanized

NR at low temperature becomes zero in a comparatively short timescale.

The changes of stress and volume of peroxide vulcanized NR sample by

extension at –26°C are measured simultaneously as shown in Figs 5.1 and 5.2

(Gent, 1954a). The sample was a long square bar in the dilatometer and was

stretched in the dilatometer at –26°C. At all extension ratios l = 1.5, 2.0, 2.5,

and 3.0, stress was relaxed to zero, and volume decreased significantly.

The Avrami equation can be used to analyze crystal growth in stretched

vulcanized NR. Initial polyhedral crystal growth is replaced by aciform



138



Chemistry, Manufacture and Applications of Natural Rubber

8



Stress (kg/cm2)



6



4



2



l  3.0



2.5



2.0



1.5



102

Time (min) at – 26°C



10



103



5.1 Experimental relations between stress and time at –26°C

for vulcanized NR at four extension ratios: l = 3.0, 2.5, 2.0, 1.5

(reproduced from Gent, 1954a).

0



–DV /V %



1

l  3.0



2.5



1.5



1.0



2







102

103

Time (min) at – 26°C



104



5.2 Experimental relations between decrease in volume, decrease

in stress and time at –26°C for vulcanized NR. Volume change

measurements, non-filled marks, stress change measurements

(scaled approximately), filled marks (reproduced from Gent, 1954a).



growth, indicating crystal growth with increased extension (Gent, 1954a);

crystal growth thus results in stress relaxation. Polyhedral crystal may be

related to TIC and aciform crystal may be induced by strain (and thence SIC).

The two-step crystallization during stress relaxation has been characterized

by Tosaka et al. (2006, 2012). In the first stage, the extended low molecular

weight chains form a crystalline nucleus, while in the second stage, amorphous

molecules attach to the nucleus and the crystal grows. Wide angle X-ray



The effect of SIC on the physical properties of NR



139



diffraction (WAXD) patterns during stress relaxation at strain 4.0 of sulfur

vulcanized NR shows that SIC increases with time at 30°C in Fig. 5.3

(Toki et al., 2005). Normalized stress readings refer to a sample’s stress

measurement, divided by the stress measurement of the sample when it is

stretched and fixed at strain 4.0 at 30°C. WAXD images show increased

crystalline fraction; since peaks in WAXD images are proof of crystalline

order in a sample, the extent of SIC is defined in these images, and crystalline

fraction and oriented amorphous fraction may be calculated.

WAXD imaging of NR at decreasing temperatures (at a rate of 2°C per

minute from 30°C) shows increased SIC, and significantly decreased stress

at lower temperatures (Fig. 5.4). The increase of SIC at lower temperature

clearly reduces stress; this is comparable to the data in Fig. 5.1. Gent wrote

that SIC increases extension, since the length of extended chains in the

crystalline unit is greater than those of oriented amorphous chains. This

reduction in stress is greater than the (predicted?) stress relative to the

absolute temperature (°K), since the number of amorphous chains decreases

with crystallization.

WAXD imaging of NR at increasing temperatures (at a rate of 2°C

per minutes from 30°C) shows the decrease of SIC and increased stress



1.3



Normalized stress



1.2

1.1

1.0

0.9

0.8

Strain 4.0 at 30°C



0.7

0.6





0



10



20

30

Time (min)



40



50



5.3 The normalized stress during relaxation process and selected 2D

WAXD patterns in vulcanized IR at 30°C. Each image was taken at the

corresponding time indicated by the arrow (reprinted from Toki et al.,

2005, with permission from the American Chemical Society).



140



Chemistry, Manufacture and Applications of Natural Rubber



Normalized stress



1.1

1.0

0.9



T/To



0.8

0.7

0.6

Strain = 4.0



0.5

30



20



10

0

–10

Temperature (°C)



–20



–30



5.4 The normalized stress as a function of temperature at strain 4.0

during constrained cooling and selected 2D WAXD patterns. Each

image was taken at the corresponding temperature indicated by the

arrows. The straight line represents the expected value calculated

by the entropy modulus following the theory of rubber elasticity

(reprinted from Toki et al., 2005, with permission from the American

Chemical Society).



(Fig.  5.5). The stress increases with the absolute temperature (°K) below

80°C, following the theory of rubber elasticity (network degradation may

occur above 80°C). Therefore, the melting of SIC increases the amount of

amorphous molecular chains, so increasing stress. But it is interesting that

the stress increases follow the linear line of absolute temperature; this means

that the increased quantity of amorphous chains does not contribute to the

stress increase, but that the original amorphous molecules increase movement

to increase the stress, following the theory of rubber elasticity. It is still not

clear whether the increased quantity of amorphous chains or the increased

thermal movement of the originally present amorphous chains contributes

to the increase of stress at higher temperature.

Stress relaxation, and the increased crystalline fraction of vulcanized NR

at room temperature as a function of time, are also shown in Fig. 5.6 (Rault

et al., 2006). Stress decreases with time at each draw ratio in Fig. 5.6(a).

At draw ratio 4.5, the crystalline fraction (c %) increases and the stress (s

(MPa)) decreases with time in Fig. 5.6(b). The increase of SIC relaxes the

remaining amorphous chains (modeled schematically in Fig. 5.7). The relaxed

amorphous chain decreases stress, due to the increased number of possible

polymeric conformations. The author proposed that the crystals become



The effect of SIC on the physical properties of NR



141



Normalized stress



1.4



1.2



1.0



0.8



0.6



Strain 4.0

20



40



60

80

Temperature (°C)



100



120



5.5 The normalized stress as a function of temperature at strain 4.0

during constrained heating and selected 2D WAXD patterns. Each

image was taken at the corresponding temperature indicated by the

arrows. The straight line represents the expected value calculated

by the entropy modulus following the theory of rubber elasticity

(reprinted from Toki et al., 2005, with permission from the American

Chemical Society).



super network points, in the same way as a filler network of carbon blacks

(Rault et al., 2006).

In the case of plastics, stress relaxation occurs due to plastic flow, which

is the mutual slippage of chains. In the case of an ideal rubber, which is

composed of an elastic network, no stress relaxation should occur, since no

viscous component should exist. To distinguish between the viscous term and

the effect of SIC in vulcanized NR, quick stretching is necessary (Tosaka, 2009;

Tosaka et al., 2006, 2012). When the entire specimen is deformed uniformly

at a strain rate of 25 min–1, the overall changes of stress and corresponding

WAXD intensities are measured by synchrotron X-ray. Stress relaxation,

after quick extension to strain 6.0 and the X-ray diffracted intensity at (200)

reflection in WAXD measurement, is shown in Figs 5.8 and 5.9 (Tosaka,

2009; Tosaka et al., 2012). Stress relaxation (Fig. 5.8) and SIC (Fig. 5.9)

start instantaneously after deformation. Vulcanized NR relaxes faster and

shows SIC earlier than vulcanized IR. SIC contributes 65–95% of the total

magnitude of post-stretch stress relaxation for vulcanized NR. The speed

of SIC has been estimated to be around 60 msec by thermo-measurement

(Mitchell and Meier, 1968). According to Tosaka, the time constants of the



142



Chemistry, Manufacture and Applications of Natural Rubber

30



Force(N)



NR 1.2g



6.40



20



6

5.8

5.5



10



3.7

lmax



0



log(t)(s)

0



1.5



2



(a)



4



s (MPa) NR = 1.2g l = 4.5

T = 23°C



6



c (%)



7

6

5

4

3

2



t (min)



1.0





1



10



(b)



100



1

1000



5.6 (a) Variation of force of vulcanized NR (1.2 g) at room

temperature as a function of different draw ratio lmax between 3.7

and 6.4. (V = 0.035 mm/s). (b) Variation of the stress and crystallinity

during stress relaxation. The sample has been previously drawn at

lmax = 4.5 (reproduced from Rault et al., 2006, with permission from

Springer).



SIC are between 50 and 200 msec (Tosaka et al., 2012). Therefore, SIC is

a very fast process, outstripping the stretching ability of ordinary stretching

machines.

The theoretical treatment of SIC has been extensive (Flory, 1947; Yamamoto

and White, 1971; Tosaka, 2009). Flory discussed the thermodynamic state

in which rubber chains are in equilibrium, and their deformed state, i.e.

stress relaxation. Entropy of rubber molecules is reduced by deformation,

and the phase transition from amorphous to crystal is caused by the rise of

melting temperature, i.e. super cooling condition due to deformation. The



The effect of SIC on the physical properties of NR



143



r(Nc) = lr0(Nc)

Nc



s0

Stretched amorphous chain



s < s0



r(Nc–nc) = lr0(Nc – nc)

n0



Nc – nc



Crystalline chain



Partially relaxed



5.7 Schematic model: role of crystallites during crystallization:

relaxation of the amorphous chains (reproduced from Rault et al.,

2006, with permission from Springer).



Normalized stress, sa(t)/sa(0)



1



0.9



0.8



0.7



a=6

NR2

NR4



NR2

NR4



IR2

IR4



IR2

IR4

0.6

0.01



1

100

Elapsed time, t (sec)



10000



5.8 Time-dependent change of normalized tensile stress of the NR

and IR samples. The tensile data were collected simultaneously

with the WAXD patterns. The samples were quickly stretched up to

6 times the original length and kept at that length (reprinted from

Tosaka, 2009, with permission of the American Chemical society).



created crystal is considered an extended chain crystal (longitudinal growth

of crystallites), with reduced tension (Flory, 1947). This is confirmation that

stress relaxation of vulcanized NR occurs mainly due to SIC.

If stress relaxation experiments were conducted under the condition of no

change of volume by pressure, energy elasticity (fe) and entropy elasticity



Chemistry, Manufacture and Applications of Natural Rubber

Intensity around 200 reflection (a.u.)



144



1.06

NR2

1.05

1.04



a=6



NR4

IR2

IR4



1.03

1.02

1.01



IR2

NR2



IR4



NR4



1.00

0.99

0.01



1

100

Elapsed time, t (sec)



10000



5.9 Time-dependent change of integrated intensity around 200

reflection in the WAXD patterns of the NR and IR samples. The

larger intensity indicates the greater development of strain-induced

crystallization. The solid lines are guides for eyes. The samples were

quickly stretched up to 6 times the original length and kept at that

length (reprinted from Tosaka, 2009, with permission of the American

Chemical Society).



(fs) at higher than room temperature could be discussed theoretically.

According to Erman and Mark (1997), the fe of vulcanized NR has been

observed to account for less than 20% of total force. Since fe/f is independent

of strain level, temperature and deformation style, network elasticity could

be postulated as an intra-molecular effect, with inter-molecular interactions

being essentially independent of chain configuration and network deformation.

However, vulcanized NR shows SIC from the small strain (less than 200%),

seemingly implicating inter-molecular interaction and volume change.



5.4



Stress–strain relation and SIC



SIC of vulcanized NR at different strains under uniaxial deformation has

been analyzed extensively, with methods including birefringence (Treloar,

1946), dilatometry (Gent, 1954a), TEM (Andrews, 1964; Luch and Yeh,

1972; Shimizu et al., 1998), X-ray (Mitchell, 1984; Lee and Donovan, 1987;

Luch and Yeh, 1973a; Toki et al., 2000; Trabelsi et al., 2003a), thermal

measurement (Mitchell and Meier, 1968), IR (Siesler, 1985), NMR (Nishi

and Chikaraishi, 1980; Komura et al., 2007; Lin et al., 2004; Kameda and

Asakura, 2003; Kimura et al., 2009; Kariyo and Stapf, 2004; Rault et al.,

2006; Che et al., 2012), Raman spectroscopy (Healey et al., 1996), and ESR

(Takagi and Ito, 2010; Toki et al., 2011; Ito and Takizawa, 2012).

Synchrotron X-ray makes it possible to measure stress–strain relations

and SIC simultaneously (Toki et al., 2002, 2005, 2008a; Che et al., 2012;



The effect of SIC on the physical properties of NR



145



Murakami et al., 2002, Trabelsi et al., 2003a, Tosaka et al., 2004, 2006,

2012). During uniaxial deformation, stress increases with strain and stress

shows an upturn at large deformation following the inverse Langevin equation

of the classic theory of rubber elasticity; SIC occurs at around 200% strain,

and stress increases until, at the final stage, breakage occurs. The hysteresis

in stress–strain relations and birefringence of vulcanized NR at 25°C under

uniaxial deformation are shown in Fig. 5.10 (Treloar, 1947). Birefringence,

expressed as n1-n2, measures total molecular orientation of amorphous and

crystal molecules. During extension, stress (tension (kg/cm2)) increases with

strain (extension ratio a). During retraction, stress decreases much lower

than the stress during extension, but the molecular orientation decreases

much higher than that during extension. The hystereses of these are opposite

behaviors.

WAXD intensity of the (120) plane of the crystal cell of vulcanized NR

and IR – and the stress–strain relation – are measured simultaneously by a

conventional X-ray instrument (Toki et al., 2000). The behavior of WAXD

intensity on the (120) plane shows the same hysteresis as described above for

birefringence. Crystal diffraction intensity increases with strain levels above

approximately 200% during extension. The stress during retraction decreases

much less than during extension; therefore, the hysteresis of birefringence

and WAXD intensity are caused mainly by SIC.

Selected WAXD patterns at strains during extension and retraction with

the stress–strain relation of vulcanized NR by synchrotron X-ray are shown

in Fig. 5.11 (Toki et al., 2002, 2003, 2004a). Oriented amorphous and crystal

fractions increase with strain during extension; both decrease during retraction,

where the fractions during retraction are larger than during extension. When



10



20



A



5



15



0



10

B



(n1-n2) ¥ 103



Tension (kg/cm2)



15



5

0



1



2



3

Extension ratio



4



5



5.10 Hysteresis phenomena as shown by tension (A) and

birefringence (B) in vulcanized NR at 25°C (reproduced from Treloar,

1947).



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