**2.1 Preparation method of** *β***-modified polypropylene sheets**

The starting material was a commercial iPP with a high tacticity (98%) obtained in powder form. The weight-averaged molecular weight *Mw* and polydispersity index *Mw/Mn* determined by gel permeation chromatography were 204 <sup>10</sup><sup>3</sup> and 6.2, respectively. A *β*-nucleator prepared from an alcohol solution of pimelic acid and calcium stearate was used. The iPP powder was added to the solution, and it was dried in an oven at 373 K for 90 min.

The *β*-nucleator-added iPP powder was pressed and melted at 483 K. The samples were completely melted for 5 min between two aluminum plates prior to the application of 7.8 MPa pressure to produce specimens of approximately 0.2 mm thick. Adjustment of the degree of crystallinity in the volume fraction and the spherulite size to the same value for all the samples was made by changing the quenching temperature and the amount of the *β*-nucleators. The molten samples were allowed to equilibrate under pressure for 5 min prior to cooling. On removal from the press, the samples were plunged directly into a water bath maintained at an appropriate temperature 0, 30, 60, and 100°C and subsequently tempered for various periods at 100°C. Consequently, these procedures enabled us to achieve sample specimens having a wide range of *β*-phase contents with a constant crystallinity of about 65% and spherulite radius *R* of around 4 μm. The structural and morphological characteristics of the samples were summarized in **Table 1**. The end numeral of the sample code PP denotes the *β*-phase concentration in the crystalline

*Tensile Properties in β-Modified Isotactic Polypropylene DOI: http://dx.doi.org/10.5772/intechopen.83348*


#### **Table 1.**

Recently the number of practical studies has increased [9] because the impact

*Polypropylene - Polymerization and Characterization of Mechanical and Thermal Properties*

The mechanical properties of semicrystalline polymers such as iPP and polyethylene (PE) are governed by their morphological features which are specified by several structural variables such as the degree of crystallinity, spherulite size, crystalline thickness, and structural organization of the supermolecular structure [10]. These diversity and independencies of these structural variables make it difficult to provide a molecular or structural interpretation for the mechanical properties and deformation behavior of semicrystalline polymers [10]. Indeed, changing the thermal or processing conditions involves the concomitant modification of several structural parameters; thus, it is difficult to determine the structural origin of the change in mechanical properties as reported by Labour et al. [11]. Consequently, it is necessary to keep all the other structural parameters to be fixed to elucidate the effects of a given structural parameter on the mechanical properties. Very few studies have dealt with the mechanical properties of *β*-nucleated iPP with a wide range of *β*-phase contents, while all the other structural parameters, such as

supermolecular organization and crystallinity, are controlled. The aim of this chapter is to elucidate the influence of the *β*-phase modification on the tensile properties of iPP. For this purpose, crystallization procedures, for the production of iPP sheets having a wide range of *β*-phase contents with fixed crystallinity and spherulite size, were developed. In addition, the effects of spherulitic morphology on tensile properties were investigated by comparing the differences in deformation

**2. Structural characterization of** *β***-modified isotactic polypropylene**

in powder form. The weight-averaged molecular weight *Mw* and polydispersity index *Mw/Mn* determined by gel permeation chromatography were 204 <sup>10</sup><sup>3</sup> and 6.2, respectively. A *β*-nucleator prepared from an alcohol solution of pimelic acid and calcium stearate was used. The iPP powder was added to the solution, and it

The starting material was a commercial iPP with a high tacticity (98%) obtained

The *β*-nucleator-added iPP powder was pressed and melted at 483 K. The samples were completely melted for 5 min between two aluminum plates prior to the application of 7.8 MPa pressure to produce specimens of approximately 0.2 mm thick. Adjustment of the degree of crystallinity in the volume fraction and the spherulite size to the same value for all the samples was made by changing the quenching temperature and the amount of the *β*-nucleators. The molten samples were allowed to equilibrate under pressure for 5 min prior to cooling. On removal from the press, the samples were plunged directly into a water bath maintained at an appropriate temperature 0, 30, 60, and 100°C and subsequently tempered for various periods at 100°C. Consequently, these procedures enabled us to achieve sample specimens having a wide range of *β*-phase contents with a constant crystallinity of about 65% and spherulite radius *R* of around 4 μm. The structural and morphological characteristics of the samples were summarized in **Table 1**. The end numeral of the sample code PP denotes the *β*-phase concentration in the crystalline

**2.1 Preparation method of** *β***-modified polypropylene sheets**

mechanism of isolated α- and *β*-spherulites.

was dried in an oven at 373 K for 90 min.

**72**

strength and toughness of *β*-nucleated iPP exceed those of *α*-iPP. Although many studies have compared the mechanical properties of *α*-iPP and *β*-iPP, the morphological origin of the differences in the mechanical properties has not been

clarified yet.

*Characteristics of iPP sheets.*

fraction of the iPP. In this chapter, PP0 is denoted by *α*-iPP and PP98 is denoted by *β*-iPP.

The crystalline *β*-phase content (the volume fraction of the *β*-phase in the crystalline portion) was determined from WAXD patterns. The WAXD measurements were carried out at room temperature with a Rigaku RU-200 diffractometer with Ni-filtered Cu-Kα radiation from a generator operated at 40 kV and 100 mA. The *β*-phase fraction in the crystalline part of the specimens was assessed from the ratio of the area of the main (300) *β*-phase to the sum of the areas of the four main crystalline reflections: (110), (040), and (130) from the *α*-phase plus (300) from the *β*-phase using Turner-Jones method [12].

Here, we modified the analysis method proposed by Somani et al. [13] to obtain the volume fraction of *β*-phase in the crystalline fraction quantitatively. The reflection peaks in the WAXD profiles were deconvoluted. In the WAXD profile, (110) at 14.1°, (040) at 16.9°, and (130) at 18.5° are the principal reflections (in 2*θ*) of the *α*-phase crystals of iPP, whereas (300) at 16.1° is the principal reflection of *β*-phase crystals, and are considered as the markers for *α*-phase and *β*-phase crystals, respectively. The various reflection areas were computed after subtraction of the amorphous halo.

The volume fraction of *β*-phase crystals was calculated using the following equations:

$$\phi\_{\beta} = \frac{\mathbb{S}\_{\beta(300)} \rho\_{\beta \mathbf{c}}^{-1}}{\mathbb{S}\_{\beta(300)} \rho\_{\beta \mathbf{c}}^{-1} + k \mathbb{S}\_{\mathbf{a}} \rho\_{\mathbf{ac}}^{-1}} \tag{1}$$

and

$$\mathcal{S}\_a = \mathcal{S}\_{a(110)} + \mathcal{S}\_{a(040)} + \mathcal{S}\_{a(130)} \tag{2}$$

Here *k* is the calibration factor, *ρβ<sup>c</sup>* (=921 kgm�<sup>3</sup> ) is the density of the *β*-phase crystal [14–16], *ρα<sup>c</sup> (*=936 kgm�<sup>3</sup> ) is the density of *α*-phase crystal [17], *S<sup>β</sup>* is the area of the (300) reflection peak, and *S<sup>α</sup>* is the sum of the areas of (110), (040), and (130) peaks of *α*-phase crystals, respectively. The calibration constant *k* was estimated to be 1.11 from the difference in the sensitivity of WAXD reflections with respect to the thickness of the sheets for the *α*-phase and *β*-phase reflections.

Crystallinity can be precisely determined from density data. The densities of the specimens were determined by the flotation method. A binary medium prepared from various ratios of distilled water and ethanol was used. The volume crystallinity can be obtained using

$$\chi\_V = \frac{\rho - \rho\_a}{\rho\_c - \rho\_a} \tag{3}$$

where *ρ* is the overall density of the sample, *ρ<sup>a</sup>* is the density of amorphous phase which was taken to be 854 kgm�<sup>3</sup> [18], and *ρ<sup>c</sup>* is the density of crystalline phase which was determined using

$$
\rho\_{\mathfrak{c}} = \phi\_{\beta}\rho\_{\beta\mathfrak{c}} + (\mathbf{1} - \phi\_{\beta})\rho\_{\mathfrak{ac}} \tag{4}
$$

where *G*<sup>0</sup> is a pre-exponential factor that is independent of temperature, *ΔH*, which is equal to 6.28 kJ/mol and corresponds to the activation energy of chain motion in

*Polypropylene*

the crystallization mechanism is divided into three regions, Regimes I, II and III,

where *Δhf* is the heat of fusion, *b*<sup>0</sup> is the thickness of the new layer, *σ* is the lateral surface free energy, *σ<sup>e</sup>* is the fold surface free energy, and *kB* is the Boltzmann constant. According to Hoffman et al. [21], the surface free energy can be estim-

*σ* ¼ Δ*hf*

where *a*<sup>0</sup> is the width of new layer, *lb* (=0.154 nm) is the bond length, *lu* (=0.1084 nm) is the projection length per atom, and *C*<sup>∞</sup> (=5.7) is the characteristic ratio [23]. The essential parameters for the kinetic study of *β* crystallization [19] are

Using Eq. 6, *logG + ΔH/*2.303*RTc* was plotted against 1/*T*Δ*Tf* as shown in **Figure 2**. Two linear parts corresponding to Regime II and Regime III were obtained: the change in the slope occurs at 401 K, which is in the range (396– 403 K) published in the literature [1], and the slope ratio is 1.74. It was estimated that *<sup>σ</sup><sup>e</sup>* = 2.68–3.08 � <sup>10</sup>�<sup>2</sup> J m�<sup>2</sup> from the slopes using *<sup>σ</sup>* of 1.4 � <sup>10</sup>�<sup>4</sup> J m�<sup>2</sup>

work of chain folding *q* can be derived from the fold surface energy given by *q* = 2*σ<sup>e</sup> a*<sup>0</sup> *b*0. Consequently, the value of *q* for the *β*-phase was estimated to be 11–13 kJ/mol, which is about half the value (28 kJ/mol) for the α-phase given by

*Kg*ð Þ<sup>I</sup> <sup>¼</sup> <sup>2</sup>*Kg*ð Þ II <sup>¼</sup> *Kg*ð Þ III <sup>¼</sup> <sup>4</sup>*b*0*σ σeT*<sup>0</sup>

is a correcting factor, and *Kg* is the nucleation constant in which

*a*0*lb luC*<sup>∞</sup>

*<sup>m</sup>* is the equilibrium melting temperature),

, *a*<sup>0</sup> = 0.636 nm, and *b*<sup>0</sup> = 0.551 nm. As a result, the

.

*<sup>m</sup>=*Δ*hf kB* (6)

(7)

. The

the melt [22], <sup>Δ</sup>*<sup>T</sup>* <sup>¼</sup> *<sup>T</sup>*<sup>0</sup>

*Tensile Properties in*

*DOI:* 

*<sup>m</sup>* þ *Tc*

*<sup>m</sup>* = 449 K, *<sup>Δ</sup>hf* = 177 MJm�<sup>3</sup>

*<sup>f</sup>* <sup>¼</sup> <sup>2</sup>*Tc<sup>=</sup> <sup>T</sup>*<sup>0</sup>

ated using

*T*0

Shi et al. [19].

**Figure 2.**

**75**

*Regime analysis of the growth rate of the* β*-spherulites.*

*<sup>m</sup>* � *<sup>T</sup>* (*T*<sup>0</sup>

 *Isotactic* 

*β-Modified*

*http://dx.doi.org/10.5772/intechopen.83348*

surface energy *<sup>σ</sup>* was estimated to be 1.4 � <sup>10</sup>�<sup>4</sup> J m�<sup>2</sup>

depending on the crystallization temperature and given by

where *ϕβ* estimated using Eq. (1) was employed.

### **2.2 Crystallization process**

The morphological feature and the growth rate of the spherulites as a function of time were examined using a polarized optical microscope during the isothermal crystallization process. A polarized optical microscope (OLYMPUS, B201) fitted with an automated hot stage was used. The hot stage (METTLER TOLEDO, FP82HT) was held at a steady temperature to �0.2 K by a proportional controller. The film including *β*-nucleators was sandwiched between a microscope slide and a cover glass, heated to 483 K and kept at this temperature for 10 min to melt the crystallites completely. Then the samples were rapidly quenched to a given crystallization temperature *Tc* and allowed to crystallize isothermally. In **Figure 1**, the growth rates of *α*and *β*-spherulites are plotted against the inverse of temperature. The growth rates increased with decreasing temperature over the whole experimental temperature ranges. **Figure 1** reveals that the difference between the two growth rates decreases with increasing temperature as shown by previous studies [6] and the growth rate of the *β*-spherulites exceeds that of the *α*-spherulite below 410 K which is slightly lower than 413–414 K determined by Shi et al. [19] and Varga [20]. This strongly suggests that the *β*-spherulites are relatively larger than the *α*-spherulites in iPP materials containing both phases prepared under usual conditions.

According to several kinetic theories [21–23], the growth rate *G* can be expressed by

$$G = G\_0 \exp\left(-\Delta H / RT\_c\right) \exp\left(-K\_\mathrm{g} / T\Delta T\!\!\!f\right) \tag{5}$$

**Figure 1.** *Temperature dependence of growth rate of* α*- and* β*-spherulites.*

where *ρ* is the overall density of the sample, *ρ<sup>a</sup>* is the density of amorphous phase which was taken to be 854 kgm�<sup>3</sup> [18], and *ρ<sup>c</sup>* is the density of crystalline phase

*Polypropylene - Polymerization and Characterization of Mechanical and Thermal Properties*

*ρ<sup>c</sup>* ¼ *ϕβρβ<sup>c</sup>* þ 1 � *ϕβ*

The morphological feature and the growth rate of the spherulites as a function of

time were examined using a polarized optical microscope during the isothermal crystallization process. A polarized optical microscope (OLYMPUS, B201) fitted with an automated hot stage was used. The hot stage (METTLER TOLEDO, FP82HT) was held at a steady temperature to �0.2 K by a proportional controller. The film including *β*-nucleators was sandwiched between a microscope slide and a cover glass, heated to 483 K and kept at this temperature for 10 min to melt the crystallites completely. Then the samples were rapidly quenched to a given crystallization temperature *Tc* and allowed to crystallize isothermally. In **Figure 1**, the growth rates of *α*and *β*-spherulites are plotted against the inverse of temperature. The growth rates increased with decreasing temperature over the whole experimental temperature ranges. **Figure 1** reveals that the difference between the two growth rates decreases with increasing temperature as shown by previous studies [6] and the growth rate of the *β*-spherulites exceeds that of the *α*-spherulite below 410 K which is slightly lower than 413–414 K determined by Shi et al. [19] and Varga [20]. This strongly suggests that the *β*-spherulites are relatively larger than the *α*-spherulites in iPP materials

According to several kinetic theories [21–23], the growth rate *G* can be

*<sup>G</sup>* <sup>¼</sup> *<sup>G</sup>*<sup>0</sup> exp ð Þ �Δ*H=RTc* exp �*Kg=T*Δ*Tf* (5)

*ρα<sup>c</sup>* (4)

which was determined using

**2.2 Crystallization process**

expressed by

**Figure 1.**

**74**

where *ϕβ* estimated using Eq. (1) was employed.

containing both phases prepared under usual conditions.

*Temperature dependence of growth rate of* α*- and* β*-spherulites.*

where *G*<sup>0</sup> is a pre-exponential factor that is independent of temperature, *ΔH*, which is equal to 6.28 kJ/mol and corresponds to the activation energy of chain motion in the melt [22], <sup>Δ</sup>*<sup>T</sup>* <sup>¼</sup> *<sup>T</sup>*<sup>0</sup> *<sup>m</sup>* � *<sup>T</sup>* (*T*<sup>0</sup> *<sup>m</sup>* is the equilibrium melting temperature), *<sup>f</sup>* <sup>¼</sup> <sup>2</sup>*Tc<sup>=</sup> <sup>T</sup>*<sup>0</sup> *<sup>m</sup>* þ *Tc* is a correcting factor, and *Kg* is the nucleation constant in which the crystallization mechanism is divided into three regions, Regimes I, II and III, depending on the crystallization temperature and given by

$$K\_{\mathbf{g}(\mathbf{l})} = 2K\_{\mathbf{g}(\mathbf{II})} = K\_{\mathbf{g}(\mathbf{III})} = 4 \, b\_0 \sigma \sigma\_\epsilon T\_m^0 / \Delta h\_f \, k\_B \tag{6}$$

where *Δhf* is the heat of fusion, *b*<sup>0</sup> is the thickness of the new layer, *σ* is the lateral surface free energy, *σ<sup>e</sup>* is the fold surface free energy, and *kB* is the Boltzmann constant. According to Hoffman et al. [21], the surface free energy can be estimated using

$$
\sigma = \Delta h\_f \frac{a\_0 l\_b}{l\_u C\_\infty} \tag{7}
$$

where *a*<sup>0</sup> is the width of new layer, *lb* (=0.154 nm) is the bond length, *lu* (=0.1084 nm) is the projection length per atom, and *C*<sup>∞</sup> (=5.7) is the characteristic ratio [23]. The essential parameters for the kinetic study of *β* crystallization [19] are *T*0 *<sup>m</sup>* = 449 K, *<sup>Δ</sup>hf* = 177 MJm�<sup>3</sup> , *a*<sup>0</sup> = 0.636 nm, and *b*<sup>0</sup> = 0.551 nm. As a result, the surface energy *<sup>σ</sup>* was estimated to be 1.4 � <sup>10</sup>�<sup>4</sup> J m�<sup>2</sup> .

Using Eq. 6, *logG + ΔH/*2.303*RTc* was plotted against 1/*T*Δ*Tf* as shown in **Figure 2**. Two linear parts corresponding to Regime II and Regime III were obtained: the change in the slope occurs at 401 K, which is in the range (396– 403 K) published in the literature [1], and the slope ratio is 1.74. It was estimated that *<sup>σ</sup><sup>e</sup>* = 2.68–3.08 � <sup>10</sup>�<sup>2</sup> J m�<sup>2</sup> from the slopes using *<sup>σ</sup>* of 1.4 � <sup>10</sup>�<sup>4</sup> J m�<sup>2</sup> . The work of chain folding *q* can be derived from the fold surface energy given by *q* = 2*σ<sup>e</sup> a*<sup>0</sup> *b*0. Consequently, the value of *q* for the *β*-phase was estimated to be 11–13 kJ/mol, which is about half the value (28 kJ/mol) for the α-phase given by Shi et al. [19].

**Figure 2.** *Regime analysis of the growth rate of the* β*-spherulites.*

curves at room temperature were measured at a constant crosshead speed of

**Figure 4a** shows the overall stress–strain curves for all the samples with various *β*-phase contents at the same crystallinity. The ultimate tensile elongation markedly increases with increasing the *β*-phase content, and the *β*-iPP (PP98) has higher drawability than *α*-iPP (PP0). The *β*-iPP is elongated more gradually with ambiguous necking as compared to *α*-iPP, which is elongated with obvious necking.

*Polypropylene*

As seen in **Figure 4b**, the initial elastic strain domain is surprisingly insensitive to the change in the composition of the crystalline phase at a fixed crystallinity. Thus, Young's modulus was constant and completely independent of the *β*-phase content (see **Figure 5**). This phenomenon is responsible for the strain concentration in the amorphous region [24] because the amorphous phase in iPP is rubberlike at room temperature and the mechanical modulus of the amorphous phase is considerably lower than those of *α*- and *β*-phase crystals. Consequently, before yielding, the deformation of the semicrystalline polymers is dominated by the deformation of the amorphous phase, indicating that the initial elastic region

The elasticity limits where the actual stress-strain curves for the *β*-modified iPP

*Stress-strain curves of iPP samples having different β-contents with a fixed crystallinity. (a) Overall curves and*

*Yield stress and Young's modulus plotted against the* β*-contents for the* β*-nucleated iPP.*

samples are deviated from the linear elastic behavior were around 0.1 strain as shown in **Figure 4b**. The deviation may be due to the onset of microscopic plastic

20 mm/min.

*DOI:* 

*Tensile Properties in*

*β-Modified*

*http://dx.doi.org/10.5772/intechopen.83348*

 *Isotactic* 

**Figure 4.**

**Figure 5.**

**77**

depends mainly on the crystallinity.

*(b) their magnification in the initial strains.*

**Figure 3.** *Lorentz-corrected SAXS patterns of iPP samples having different* β*-contents with a fixed crystallinity.*

## **2.3 Crystalline morphology**

The small angle X-ray scattering (SAXS) measurement was performed with a point-focusing optics and a one-dimensional position-sensitive proportional counter (PSPC) with an effective length of 10 cm. The CuKα radiation supplied by a MAC Science M18X generator operating at 40 kV and 30 mA was used throughout. The distance between the sample and PSPC was about 40 cm. The geometry was further checked using a chicken tendon collagen, which gives a set of sharp diffraction spots corresponding to 65.3 nm.

From the volume fraction of the crystals *χV*, and SAXS long period *Lp*, the lamellar crystal thickness *Lc* and amorphous layer thickness *La* can be determined, assuming a two-phase model, from the following relationship:

$$L\_c = \chi\_V L\_p, \qquad L\_a = (1 - \chi\_V) L\_p \tag{8}$$

**Figure 3** shows the Lorentz-corrected SAXS intensities plotted against magnitude of scattering vector *s* (= 2/*λ* sin*θ*) where 2*θ* is the scattering angle and *λ* is the X-ray wavelength (= 0.1542 nm). The maximum point in the SAXS curves yields the average long period. The *s* value of *α*-PP (or PP0) was around 0.07 nm�<sup>1</sup> , and the *s value* of *β*-iPP (or PP98) was around 0.0625 nm�<sup>1</sup> , indicating that the long period *Lp* of *β*-iPP is greater than that of *α*-iPP. The iPP samples with both modifications have two SAXS peaks corresponding to the *α*-phase peak near 0.072 nm�<sup>1</sup> and *β*-phase peak near 0.0625 nm�<sup>1</sup> . This strongly suggests that the modified iPP samples with the *α*- and *β*-spherulites coexist but no co-crystallization of *α*-phase and *β*-phase crystals takes place. The specific long periods for *α*-phase and *β*-phase were about 14 and 16 nm.
