Effect of Cyclo-Olefin Copolymer Loading on Kinetics,Thermodynamics and Model of Linear Low Density Polyethylene Crystallinity

Abstract

The behavior of kinetic and thermodynamic characteristics of linear low-density polyethylene (LLDPE) crystallinity containing cyclo-olefin copolymer (COC) were investigated by means of differential scanning calorimeter (DSC). The crystallinity kinetic parameters including the crystallinity apparent activation energy (E), rate of crystallinity constant (K) and the order of crystallinity (n) were calculated with Borchardt and Daniels methods. The results have shown that the activation energy of blends increased with increase in the COC loading and the order of crystallinity was the first order for all blends. Gibbs free energy, enthalpy and entropy of the LLDPE crystallinity increased with the loading of COC. The different crystallinity kinetic models of LLDPE were observed with the loading of COC. It was concluded that the COC hindered the chains of polymer from aligning in a row.

Keywords

Thermodynamics Crystallinity Differential Scanning Calorimetry (DSC)Modeling Polyethylene (PE)

1 Introduction

Linear low-density polyethylene (LLDPE) has valuable mechanical, electrical and optical properties. Moreover, it has excellent moisture resistance and chemical inertness, and is stiffer and harder than branched polymers, which has led to its application apply in different industries [1]. It was reported that the global consumption of polymers has increased to 95 million tons since 1950 and 42.0% of this consumption is devoted to the manufacture of packaging materials made of linear low-density polyethylene (LLDPE) and high-density polyethylene (HDPE) [2]. The Middle East production [3] capacity of LLDPE has increased 500% since 2000.

Cyclo-olefin copolymers (COCs) are of interest in molecular engineering and are a new class of engineering plastics. Many researchers have studied the synthesis and characterization of cycloolefin copolymers (COCs). Ethylene/ cycloolefin copolymers and norbornene and ethylene copolymers are amorphous glasses with random sequence distributions [4,5]. COCs have been observed to provide hardness, high chemical impedance, a perfect wet barrier, least wet intake and low-density properties. The COCs application included different disciplines such as diaphanous moldings (visual information storage, lenses and sensors), the packaging of medicine, medicinal and diagnostic equipments, nourishment vessels, etc. [6–8]. COCs have been used to create membranes for in vitro tissue models applications and the experiments showed that the membrane successfully supports cell attachment and proliferation in fibroblasts and endothelial cells [9].

Polyolefinic materials were widely used to improve the different properties of COCs. The blending polyolefin elastomer with COCs improved the toughness and flow behavior of COCs [10,11]. Kolarik et al. studied the influence of COC on the tensile characteristics of polypropylene (PP)/COC blends [12,13] and high-density polyethylene (HDPE)/COC blends [14,15]. Meanwhile, Pimbert [16] and Slouf et al. [17] investigated the crystallinity and nucleation modes of PP in PP/COC blends.

The crystal engineering of polymer materials has drawn the attention of many researchers due to their attractive architecture and potential applications such as magnetism, electric conductivity, molecular adsorption and catalysis [18]. Many parameters have an impact on the polymer crystallinity such as the composition of polymers, configuration, and molecular weight; therefore, it is patronized according to the classical nucleation theory. Thus, it suggests that the nucleation is formed by a combination of a few digits of atoms or molecules in the new solid phase followed by the growth of the nuclei. Polymeric nuclei must be shaped by a combination of macromolecular pieces and the crystallinity can grow by connection of fresh solid phase to the growth front [19].

Zhao et al. [20] was found that crystallization in the blends depends significantly on the content of branches in the LLDPE. Luyt and Hato [21] reported that a reduction in the aggregate crystallinity of LLDPE with an expansion in both LDPE and wax substance was observed. Moreover, the empirical enthalpy amounts of LLDPE in the mixtures were mostly greater than the predictable theoretical amounts. Wang et al. [22] concluded that the crystallinity of the chlorosulfonated polyethylene decreased with the increment of chlorine and sulfur content. Long et al. [23] found that the long periods and thickness of the crystalline region were greatly influenced by the addition of highly branched polyethylene. Alwaan et al. [24] found that the crystallinity of metallocene linear low density polyethylene was expanded by zinc borate (ZB) filling increment; along these lines, ZB became the focus of the heterogeneous nucleation and most extreme crystallinity was seen at 6 phr ZB mix. Alwaan et al. [25] also investigated the degree of crystallinity of the mLLDPE/rubber composites using differential scanning calorimetry (DSC). They found that the lowest crystallinity was shown in 10% rubber/ mLLDPE mixture. Non-isothermal crystallization behaviour and the crystallization kinetics of pure LLDPE and LLDPE/REDMUD blends were investigated by DSC [26].

In current work, the nonisothermal crystallinity kinetics of LLDPE material blended with different loading of COC (0–100wt%) has been investigated using Borchardt and Daniels method. The mechanism of the crystallinity, the order of crystallinity, the rate of crystallinity constant and the activation energy were calculated at different temperatures. Moreover, thermodynamics properties of LLDPE/COC blends represented by Gibbs free energy, enthalpy and entropy of crystallinity were also studied. The kinetic model for the crystallinity operation of all blends and pure materials is examined by Criado technique utilizing various solid-state procedure mechanisms. To the best of our information, there has been no systematic consideration of the impact of COC on the kinetics, thermodynamics, and model of LLDPE crystallinity.

2 Experimental

2.1 Materials

Cycloolefin copolymer (COC) is known under the trade name Topas® 8007 (Ticona company, Kelsterbach, Germany) with melt flow index (MFI) of 1.7 g/10 min at temperature of 190°C and under loading of 2.16 kg on the sample with a density equal to 1.02 g/cm³. Linear low-density polyethylene (LLDPE) (Clearflex® CL106) has been supplied by Polimeri Europa (Mantova, Italy). Its density is 0.92 g/cm³ and MFI is 3.2 g/10 min at temperature of 190°C and under loading of 2.16 kg on the sample.

2.2 Sample Preparation

Linear low-density polyethylene (LLDPE) and cycloolefin copolymer (COC) were mixed at different weight percentages of COC (0–100wt%) by milling machine (Double Elephants Brand SX-160, China) at a temperature of 190°C for 15 min until the homogenous blends were obtained. The blends were compression molded at 190°C under a pressure of 10 MPa for the time period of 15 min into sheets with a thickness between 2.5–3 mm. These blends were used for differential scanning calorimeter (DSC) tests to analyse the crystallinity of the blends. The formula of the LLDPE/COC blends is shown in Table 1 .

Table 1
The formula of the LLDPE/COC blends (wt%)

Sample code LLDPE COC

A0 100 0

A20 80 20

A40 60 40

A50 50 50

A60 40 60

A80 20 80

A100 0 100

Sample code	LLDPE	COC
A0	100	0
A20	80	20
A40	60	40
A50	50	50
A60	40	60
A80	20	80
A100	0	100

2.3 Differential Scanning Calorimeter (DSC)

The crystallinity of the blends was studied using a DSC7 analyzer (Perkin-Elmer, made in U.S.A.). Samples were heated from room temperature to 200°C at heating rate of 10°C/min, and maintained at both temperatures of 50 and 200°C for 5 min to erase the thermal and mechanical history before cooling to temperature of 40°C at heating rate of 10°C/min under a nitrogen (N₂) current of 100 ml/min around the specimen. The temperature calibration was performed using indium (T_m = 156.6°C, ΔH_m = 28.45 kJ kg⁻¹) and zinc (T_m = 419.47°C, ΔH_m = 108.37 kJ kg⁻¹). Measurements were performed with the aluminium capsules of samples around 10 mg weights.

3 Results and Discussion

3.1 Kinetics

DSC gives the relationship between the heat flow (dH/dt) of the sample and temperature (T). The essential hypothesis for the implementation of DSC technique is that the rate of the kinetic operation (dα/dt) is proportional to the value of heat flow [27–29] (dH/dt). It is sensible to suppose that the kinetic parameters can be located by Borchardt and Daniels method [30], where the crystallinity rate at a specific time t is a function of the crystallinity conversion portion (α), or

\frac{d α}{d t} = K_{(T)} {(1 - α)}^{n}

(1)

where dα/dt = the rate of crystallinity, K_(T) = the rate of crystallinity constant and n = the order of crystallinity. Taking the Ln function to both sides of Eq. (1), the following equation can be obtained:

L n (\frac{d α}{d t}) = n L n (1 - α) + L n (K_{(T)})

(2)

Plotting Ln(dα/dt) versus Ln (1−α) according to Eq. (2) gives a straight line. The slope represents the order of crystallinity (n) while the intercept represents the rate of crystallinity constant (Ln(K_(T))). The crystallinity rate (dα/dt) was acquired by dividing the peak height (H) at temperature T by the total peak area (A_T), while the portion un-crystallinity (1 - α) was gained by measuring the ratio of the partial peak area (A_p) at temperature T to the total peak area (A_T) and subtracting it from unity [30]. OriginPro 8.5 was used to analyse data of DSC peaks to get the crystallinity rate (dα/dt) and un-crystallinity (1 − α) where the peak height (H) at temperature T, the partial peak area (A_p) at temperature T and the total peak area (A_T) of DSC peak were calculated by using OriginPro 8.5. Therefore, the crystallinity rate (dα/dt) and un-crystallinity (1 − α) can be estimated as the following:

Crystallinty Rate = \frac{d α}{d t} = \frac{H}{A_{T}}

(3)

Un Crystallinty Rate = (1 - α) = (1 - \frac{A_{ρ}}{A_{T}})

(4)

Excel program was used to plot crystallinity rates logarithm versus un-crystallinity's logarithm, as well as to obtain linear regression lines with the corresponding equations and correlation coefficients (R²). Figure 1 shows the DSC peaks of pure LLDPE and its blends acquired at temperatures ranging from 100 to 140°C. The crystallinity order n and K_(T) were gained from the drawing of ln(dα/dt) versus ln(1 - α), as shown in Figure 2 .

The rate of crystallinity equations of A0, A20, A40, A50, A60 and A80 blends were obtained from Figure 2 , as shown below:

\begin{matrix} L n (\frac{d α}{d t}) = 0.7122 L n (1 - α) - 3.1792 & R^{2} = 0.9532 & For A0 \end{matrix}

(5)

\begin{matrix} L n (\frac{d α}{d t}) = 0.7432 L n (1 - α) - 3.1489 & R^{2} = 0. 9421 & For A20 \end{matrix}

(6)

\begin{matrix} L n (\frac{d α}{d t}) = 0. 6626 L n (1 - α) - 3.1623 & R^{2} = 0.9362 & For A40 \end{matrix}

(7)

\begin{matrix} L n (\frac{d α}{d t}) = 0. 5774 L n (1 - α) - 3.1524 & R^{2} = 0.9079 & For A50 \end{matrix}

(8)

\begin{matrix} L n (\frac{d α}{d t}) = 0. 5883 L n (1 - α) - 3.2759 & R^{2} = 0.854 & For A60 \end{matrix}

(9)

\begin{matrix} L n (\frac{d α}{d t}) = 1. 0905 L n (1 - α) - 2.1788 & R^{2} = 0.9572 & For A80 \end{matrix}

(10)

The order of crystallinity of pure LLDPE and its blends changed from 0.5774th to 1.0905th, as shown in Eqs. (5)–(10). Therefore, the crystallinity is likely to be the first order. Moreover, the fitting lines of blends are almost parallel to each other except the A80 blend, therefore it may be concluded that the crystallinity of pure LLDPE, A20, A40, A50 and A60 blends indicated similar nucleation mechanism and crystal growth geometries, while A80 blend has different mechanism and crystal growth geometries from other blends.

The activation energy (E) can be found by employing the Arrhenius expression, as shown below, and the results were shown in Figure 3 .

K = A e^{- \frac{E}{R T}}

(11)

L n (K) = - \frac{E}{R T} + L n (A)

(12)

where E is the activation energy of crystallinity, T is the absolute temperature and R is the universal gas constant (8.314 J/mol.K).

From the slope of a linear fit line, the activation energy of crystallinity (E/R) can be estimated, i.e., plotting of Ln(K) versus (1/T) according to Eq. (12) produces a straight line, in which its slope represents the activation energy of crystallinity (E/R) and its intercept represents the pre-exponential factor (A), as shown in Figure 3 and Eqs. 13–18.

The rate of crystallinity constant equations at different loading of COC (0–80wt %) were reported below:

\begin{matrix} L n (K) = \frac{2.9359}{T} - 10.757 & R^{2} = 0979 & For A 0 \end{matrix}

(13)

\begin{matrix} L n (K) = \frac{3.1439}{T} - 11.275 & R^{2} = 0.9251 & For A2 0 \end{matrix}

(14)

\begin{matrix} L n (K) = \frac{5.7261}{T} - 18.189 & R^{2} = 0.961 & For A4 0 \end{matrix}

(15)

\begin{matrix} L n (K) = \frac{8.2441}{T} - 24.678 & R^{2} = 0.9307 & For A5 0 \end{matrix}

(16)

\begin{matrix} L n (K) = \frac{6.9771}{T} - 21.574 & R^{2} = 0.9154 & For A6 0 \end{matrix}

(17)

\begin{matrix} L n (K) = \frac{16.623}{T} - 46.296 & R^{2} = 0.8654 & For A8 0 \end{matrix}

(18)

The activation energy of LLDPE crystallinity was increased by the increase of COC loading in the blends, as shown in Eqs. 13 to 18 and Figure 4 . The activation energy of A80 blend was highest and it is more than five times that of pure LLDPE. The reason may be the loading of 80wt% COC deviates mechanism and crystal growth geometries of LLDPE from other blends as concluded in the previous discussion. Moreover, it can be concluded that the COC impedes the nucleation and crystal growth geometries of LLDPE blends.

The crystallinity activation energy is closely related to crystallinity process, and can display the crystallinity ability being high or not (high E value reveals low crystallinity ability). The total crystallization operation is normally consisted of concurrent nucleation and growth steps with loading COC. It is fully recognized that the macromoleculars of polymer in the melt have relatively high viscosity and low diffusivity. Therefore, the macromoleculars of polymer or segments must pass specific energy hindrances to diffuse and attach onto the growing front of a crystal. While the COC is inserted into LLDPE matrix, the nucleation process of LLDPE/COC blends is hindered. Thus, the crystallinity activation energy of LLDPE/COC blends is higher than that of virgin LLDPE. Kolarik et al. [31] found that crystallinity of the HDPE in blends reduces relative to its weight fraction of COC from 69% for the virgin HDPE to 59% for the 25/75 HDPE/COC blend. In addition, the pre-exponential factor (A) was also increased by the increase in COC loading, as shown in the previous Eqs. 13–18.

3.2 Crystallinity Thermodynamics

The transition state equation [32–34] is:

\frac{d α}{d t} = r = \frac{R T}{N . h} * E X P (\frac{Δ S °}{R}) * E X P (- \frac{Δ H °}{R T})

(19)

where r the rate of crystallinity (dα/dt = H/A_T), ΔH° the enthalpy of activation at the standard condition, ΔS° the entropy of activation at the standard condition, h the Planck's constant and N the Avogadro number.

The rearrangement of Eq. (19) produces Eq. (20):

\frac{r}{T} = M * E X P (- \frac{Δ H °}{R T})

(20)

where M = R/Nh * EXP(ΔS°/R)

Taking the (Ln) function to both sides of Eq. (20) gets Eq. (21):

L n (\frac{r}{T}) = - \frac{Δ H °}{R T} + L n (M)

(21)

According to Eq. (21), the plotting of the Ln(r/T) against 1/T gives a straight line. The slope of the straight line represents ΔH°/R and the intercept represents Ln(M) which M is equal to (R/Nh * EXP(ΔS°/R). Figure 5 shows the relationship of crystallinity rate Ln(r/T) and inverse temperature (1/T)°K of pure LLDPE and its blends.

The following are the equations of straight line that were obtained from Figure 5:

\begin{matrix} L n (\frac{r}{T}) = - \frac{5.8372}{T} + 5.1251 & R^{2} = 0.9688 & For A0 \end{matrix}

(22)

\begin{matrix} L n (\frac{r}{T}) = - \frac{6.1952}{T} + 6.3172 & R^{2} = 0.9526 & For A20 \end{matrix}

(23)

\begin{matrix} L n (\frac{r}{T}) = - \frac{6.8388}{T} + 8.0231 & R^{2} = 0.9486 & For A40 \end{matrix}

(24)

\begin{matrix} L n (\frac{r}{T}) = - \frac{7.5949}{T} + 10.07 & R^{2} = 0.9339 & For A50 \end{matrix}

(25)

\begin{matrix} L n (\frac{r}{T}) = - \frac{5.552}{T} + 4.6711 & R^{2} = 0.9054 & For A60 \end{matrix}

(26)

\begin{matrix} L n (\frac{r}{T}) = - \frac{11.246}{T} + 19.44 & R^{2} = 0.8775 & For A80 \end{matrix}

(27)

Therefore, from Eqs. 22, 23, 24, 25, 26 and 27, the average enthalpy (ΔH°) is equal to 59.95 J/mol while the average Ln((R/Nh * EXP(ΔS°/R)) is equal to 8.9411.

On the other hand, Gibbs free energy can be calculated as the following [35]:

Δ G = - R T L n K

(28)

Substitute Eq. (13) in Eq. (28) to obtain:

\begin{matrix} Δ G = R T (\frac{2.9359}{T} - 10.757) & For & A0 \end{matrix}

(29)

A similar procedure applies for Eq. (12) to (16) to find:

\begin{matrix} Δ G = R T (\frac{3.1439}{T} - 11.275) & For & A 20 \end{matrix}

(30)

\begin{matrix} Δ G = R T (\frac{5.7261}{T} - 18.189) & For & A 40 \end{matrix}

(31)

\begin{matrix} Δ G = R T (\frac{8.2441}{T} - 24.678) & For & A 50 \end{matrix}

(32)

\begin{matrix} Δ G = R T (\frac{6.9771}{T} - 21.574) & For & A 60 \end{matrix}

(33)

\begin{matrix} Δ G = R T (\frac{16.623}{T} - 46.296) & For & A 80 \end{matrix}

(34)

To find the enthalpy and entropy of crystallinity as a function of the temperature needed to align the chains of LLDPE, the Gibbs-Helmholtz equations [35] were used, as the following:

{[\frac{\partial (\frac{Δ G}{T})}{\partial T}]}_{p} = \frac{- Δ H}{T^{2}}

(35)

If Eqs. (29) to (34) are divided by T and derivative by ∂T, the results should be equal to (-ΔH/T²) according to Eq. (35), as the following:

\begin{matrix} {[\frac{\partial (\frac{Δ G}{T})}{\partial T}]}_{p} = \frac{2.9359 R}{- T^{2}} = \frac{- Δ H}{T^{2}} & For & A 0 \end{matrix}

(36)

\begin{matrix} {[\frac{\partial (\frac{Δ G}{T})}{\partial T}]}_{p} = \frac{3.1439 R}{- T^{2}} = \frac{- Δ H}{T^{2}} & For & A2 0 \end{matrix}

(37)

\begin{matrix} {[\frac{\partial (\frac{Δ G}{T})}{\partial T}]}_{p} = \frac{5.7261 R}{- T^{2}} = \frac{- Δ H}{T^{2}} & For & A4 0 \end{matrix}

(38)

\begin{matrix} {[\frac{\partial (\frac{Δ G}{T})}{\partial T}]}_{p} = \frac{8.2441 R}{- T^{2}} = \frac{- Δ H}{T^{2}} & For & A5 0 \end{matrix}

(39)

\begin{matrix} {[\frac{\partial (\frac{Δ G}{T})}{\partial T}]}_{p} = \frac{6.9771 R}{- T^{2}} = \frac{- Δ H}{T^{2}} & For & A6 0 \end{matrix}

(40)

\begin{matrix} {[\frac{\partial (\frac{Δ G}{T})}{\partial T}]}_{p} = \frac{16.623 R}{- T^{2}} = \frac{- Δ H}{T^{2}} & For & A8 0 \end{matrix}

(41)

Thus, the results of enthalpy are observed in Table 2:

Table 2

The crystallinity enthalpies (J/mol) of blends

Composites	A0	A20	A40	A50	A60	A80
ΔH(J/mol)	24.41	26.14	47.61	68.54	58.01	138.20

From the results of enthalpy, it was clearly observed that the enthalpy increased with the loading of COC, therefore it can be concluded that the COC obstructed the chains of polymer from aligning in a row. These results agree with results of activation energy.

Meanwhile, the entropy of the blends can be found by the following Gibbs-Helmholtz Eq. [35]:

{(\frac{\partial Δ G}{\partial T})}_{p} = - Δ S

(42)

To obtain the ΔS values of pure LLDPE and its blends, Eqs. 29 to 34 should derive by ∂T and the results should be equal to (-ΔS) according to Eq. (42), as the following:

\begin{matrix} {(\frac{\partial Δ G}{\partial T})}_{p} = - 10.757 R = - Δ S & For & A 0 \end{matrix}

(43)

\begin{matrix} {(\frac{\partial Δ G}{\partial T})}_{p} = - 11.275 R = - Δ S & For & A2 0 \end{matrix}

(44)

\begin{matrix} {(\frac{\partial Δ G}{\partial T})}_{p} = - 18.189 R = - Δ S & For & A4 0 \end{matrix}

(45)

\begin{matrix} {(\frac{\partial Δ G}{\partial T})}_{p} = - 24.678 R = - Δ S & For & A5 0 \end{matrix}

(46)

\begin{matrix} {(\frac{\partial Δ G}{\partial T})}_{p} = - 21.574 R = - Δ S & For & A6 0 \end{matrix}

(47)

\begin{matrix} {(\frac{\partial Δ G}{\partial T})}_{p} = - 46.296 R = - Δ S & For & A8 0 \end{matrix}

(48)

The results of entropy of all blends are shown in Table 3:

Table 3

The entropies (J/mol) of A0, A20, A40, A50, A60 and A80 blends

Composites	A0	A20	A40	A50	A60	A80
ΔS(J/mol)	89.43	93.74	151.22	205.17	179.37	384.91

It was clearly shown that the entropy increased with the loading of COC. Thus, the disorder of LLDPE chains increased with the loading of COC, meaning that the crystallinity is not easy to form with increase in COC loading. Therefore, it can be concluded that the COC hindered the chains of polymer from aligning in a row. These results agree with both previous results of activation energy and enthalpy.

3.3 Crystallinity Model

To find the crystallinity kinetic model of blends, the Criado mode was selected, as this includes crystallinity mechanisms. The models and expressions [36,37] of associated function g(α) and f(α) are shown in Table 4 .

Table 4
Solid-state rate expressions for different models, classifications and mathematical derivations [36,37]

Model Differential form f(α) = (1/k) dα/dt Integral form g(α) = kt

Nucleation models

Power law (P2) 2α^(1/2) α^(1/2)

Power law (P3) 3α^(2/3) α^(1/3)

Power law (P4) 4α^(3/4) α^(1/4)

Avarami-Erofeyev (N2) 2(1−α) [−ln(1−α)]^1/2 [−ln(1−α)]^1/2

Avarami-Erofeyev (N3) 3(1−α)[−ln(1−α)]^2/3 [−ln(1−α)]^1/3

Avarami-Erofeyev (N4) 4(1−α)[−ln(1−α)]^3/4 [−ln(1−α)]^1/4

Geometrical contraction models

Contracting area (R2) Contracting volume (R3) 2(1−α)^1/2 [1-(1−α)^1/2]

3(1−α)^2/3 [1-(1−α)^1/3]

Diffusion models

1-D Diffusion (D1) 1/(2α) a²

2-D Diffusion (D2) [−ln(1−α)]⁻¹ [(1−α)ln(1−α)] + α

3-D Diffusion-Jander (D3) [3(1−α)^2/3]/[2(1−(1−α)^1/3)] [1-(1−α)^1/3]²

Reaction-order models

First-order (F1) (1−α) -ln(1−α)

Second-order (F2) (1−α)² (1−α)⁻¹-1

Model	Differential form f(α) = (1/k) dα/dt	Integral form g(α) = kt
Power law (P2)	2α^(1/2)	α^(1/2)
Power law (P3)	3α^(2/3)	α^(1/3)
Power law (P4)	4α^(3/4)	α^(1/4)
Avarami-Erofeyev (N2)	2(1−α) [−ln(1−α)]^1/2	[−ln(1−α)]^1/2
Avarami-Erofeyev (N3)	3(1−α)[−ln(1−α)]^2/3	[−ln(1−α)]^1/3
Avarami-Erofeyev (N4)	4(1−α)[−ln(1−α)]^3/4	[−ln(1−α)]^1/4
Geometrical contraction models
Contracting area (R2) Contracting volume (R3)	2(1−α)^1/2	[1-(1−α)^1/2]
	3(1−α)^2/3	[1-(1−α)^1/3]
Diffusion models
1-D Diffusion (D1)	1/(2α)	a²
2-D Diffusion (D2)	[−ln(1−α)]⁻¹	[(1−α)ln(1−α)] + α
3-D Diffusion-Jander (D3)	[3(1−α)^2/3]/[2(1−(1−α)^1/3)]	[1-(1−α)^1/3]²
Reaction-order models
First-order (F1)	(1−α)	-ln(1−α)
Second-order (F2)	(1−α)²	(1−α)⁻¹-1

The z(α) master plots are obtained by joining the differential and integral styles of the models [38,39]. The kinetic model of the operation can be located by representing the z(α) function as:

Z (α) = f (α) g (α) = {(\frac{d α}{d t})}_{α} T_{α}^{2} [\frac{π (x)}{β T_{α}}]

(49)

where × = E/RT. Therefore, the amounts of z(α) can be located for each amount of a by multiplying the experimental amounts of (dα/dt)_α and T_α². It has been confirmed [36] that the expression in the brackets of Eq. (49) has a negligible effect on the shape of the z(α) function. The calculation of the crystallinity rate (dα/dt) and crystallinity fraction (α) at temperature T from experimental data have been previously described. Thus, these data can be used to find the result of multiplying the experimental amounts of (dα/dt)_α and T_α² to locate the amounts of the experimental z(α) for each amount of a. Moreover, the theoretical z(α) plots are gained by plotting the product of f(α)g(α) in Table 4 versus a using experimental data of a for different reaction models. Therefore, the master curves of pure LLDPE and its blends can be found by dividing the amount of Z(α) for each value of α by the amount of Z(α) at α = 0.5 and the result is plotted versus a according to Criado method. The master curves of pure LLDPE and its blends are shown in Figure 6 .

The resulting experimental amounts of z(α) are plotted as a function of a, as compared against theoretical z(α) master plots. An appropriate model is recognized as the best match between the experimental and theoretical z(α) master plots. From a comparison of the experimental master plots of A0, A20, A40, A50, A60 and A80 blends with theoretical, it was found that the best described crystallinity kinetic models of pure LLDPE and its blends are reported in Table 5 .

Table 5

The crystallinity kinetic model of A0, A30, A40, A50, A60 and A80 blends

Materials	Crystallinity kinetic model
A0	R2
A20	D3
A40	D3
A50	D3
A60	D3
A80	D3

It was observed that pure LLDPE follows the contracting area (R2) model while LLDPE/COC blends obey the D Diffusion-Jander (D3) model. It may be concluded that the increase in activation energy of LLDPE crystallinity with loading of the COC causes the transfer of the crystallinity kinetic models of LLDPE from contracting area (R2) model to the D diffusion-jander (D3) model.

4 Conclusions

The effect of COC on the crystallinity kinetics, thermodynamics properties, and crystallinity model of LLDPE was investigated. It was concluded that the crystallinity of pure LLDPE and its blends have a similar nucleation mechanism and crystal growth geometries for all blends except at the loading of 80wt% COC which causes to deviate the mechanism and crystal growth geometries of LLDPE from other blends. It was found that the order of crystallinity kinetics of pure LLDPE and its blends are first order. Moreover, the COC hinders the nucleation and crystal growth geometries of LLDPE blends. The disorder of LLDPE chains increased with the loading of COC and the crystallinity is not easy to form in the presence of COC. Increasing loading of COC leads to increase Gibbs free energy, enthalpy and entropy of the LLDPE crystallinity. The COC is the impact factor of the crystallinity kinetic model of LLDPE, which transfers the crystallinity kinetic models of LLDPE from contracting area (R2) model to the D Diffusion-Jander (D3) model.

References

Sarker

, Dey

, and Khan

R.A.

, J Thermoplast. Compos. Mater., 24, (2011), 679–694.

Santos

M.F.

, Machado

, Tachinski

C.G.

, Júnior

J.F.

, Piletti

, Peterson

, and Fiori

M.A.

, Mater. Sci. Eng. C, 39, (2014), 403–410.

Al-Salem

S.M.

, Abraham

, Al-Qabandi

O.A.

, and Dashti

A.M.

, Polym. Testg., 46, (2015), 116–121.

Lavoie

A.R.

, and Waymouth

R.M.

, Tetrahedron, 60, (2004), 7147–7155.

Wang

Z.Y.

, Yue

C.Y.

, and Roy

, Polym., 53, (2012), 1932–1938.

Forsyth

, Pereña

J.M.

, Benavente

, Pérez

, Tritto

, Boggioni

, and Brintzinger

H-H.

, Macromolecular Chem. Phys., 202, (2001), 614–620.

Forsyth

J.F.

, Scrivani

, Benavente

, Marestin

, and Pereña

J.M.

, J. Appl. Polym. Sci. 82, (2001), 2159–2165.

Scrivani

, Benavente

, Pérez

, and Pereña

J.M.

, Macromolecular Chem. Phys. 202, (2001), 2547–2553.

Gela

, Kandasamy

, Cartledge

, and Haylock

, Sensors and Actuators A, 215, (2014), 51–55.

10.

Khanarian

, Polym. Eng. Sci., 40, (2000), 2590–2601.

11.

Jafari

S.H.

, Hesabi

M.N.

, Khonakdar

H.A.

, and Asl-Rahimi

, J. Polym. Res. 18, (2011), 821–832.

12.

Kolarík

, Pegoretti

, Fambri

, and Penati

, Macromolecular. Mater. Eng. 288, (2003), 629–641.

13.

Pegoretti

, Kolarík

, Fambri

, and Penati

, Polym., 44, (2003), 3381–3387.

14.

Kolarík

, Kruli

, Slouf

, and Fambri

, Polym. Eng. Sci. 45, (2005), 817–826.

15.

Kolarík

, Pegoretti

, Fambri

, and Penati

, Polym. Eng. Sci., 46, (2006), 1363–1373.

16.

Pimbert

, Macromolecular Symposia, 203, (2003), 277–283.

17.

Slouf

, Kolaík

, and Fambri

, J. Appl. Polym. Sci., 91, (2004), 253–259.

18.

Xiao

, Gu

, and Xue

, J. Crystal Growth, 311, (2009), 601–604.

19.

Raimo

, Prog. Crystal Growth Characterization Mater., 57, (2011), 65–92.

20.

Zhao

, Liu

, and Yang

, Macromol. Chem. Phys., 198, (1997), 1427–1436.

21.

Luyt

A.S.

, and Hato

M. J.

, J. Appl. Polym. Sci., 96(5), (2005), 1748–1755.

22.

Wang

, Ni

, Bian

, Zhang

, and Zhang

, J. Appl. Polym. Sci., 116, (2010), 2095–2100.

23.

Long

Y.-Y.

, Liu

S.-R.

, Cui

, and Li

Y.-S.

, J. Appl. Polym. Sci., 115, (2010), 3045–3055.

24.

Alwaan

I. M.

, and Hassan

, Iran Polym. J. 23, (2014), 277–287.

25.

Alwaan

I. M.

, Hassan

, and Piah

M. A. M.

, Polymers & Polym. Composit., 23(7), (2015), 495–502.

26.

, Cao

, Huo

, Luo

, He

, Polymers and Polym. Composit, 23(7), (2015), 483–494.

27.

Varma

I.K.

, and Bhama

P.V.S.

, J. Composite Mater., 20, (1986), 410–422.

28.

, Thermochim Acta, 367–368, (2001), 101–106.

29.

Rosu

, Cascaval

C.N.

, Mustata

, and Ciobanu

, Thermochim Acta, 383, (2002), 119–127.

30.

Borchardt

H.J.

, and Daniels

, J. American Chemical Society, 79, (1957), 41–46.

31.

Martinez-Camacho

A.P.

, Cortez-Rocha

M.O.

, Graciano-Verdugo

A.Z.

, Rodriguez-Félix

, Castillo-Ortega

M.M.

, Burgos-Hernndez

, Ezquerra-Brauer

J.M.

, and Plascencia-Jatomea

, Carbohydrate Polym., 91, (2013), 666–674.

32.

Ostovari

, Hoseinieh

S.M.

, Peikari

, Shadizadeh

S.R.

, and Hashemi

S.J.

, Corro. Sci., 51(9), (2009), 1935–1949.

33.

Singh

A.K.

, and Quraishi

M.A.

, Corro. Sci., 52(1), (2010), 152–160.

34.

Alwaan

I.M.

, International J. Chem. Eng., 2014, (2014), 1–7.

35.

Atkins

, and de Paula

, Atkins’ Physical Chemistry. 8th ed, p. 107, Oxford University Press: United Kingdom, (2006).

36.

Alwaan

I.M.

, and Hassan

, Prog. Rubb. plastics & recycling technology J., 30(3), (2014), 153–168.

37.

Singh

, Soni

P.K.

, Singh

, and Srivastava

, Thermochimica Acta, 548, (2012), 88–92.

38.

Vyazovkin

, Burnham

A.K.

, Criado

J.M.

, Pérez-Maqueda

L.A.

, Popescu

, and Sbirrazzuoli

, Thermochimica Acta, 520, (2011), 1–19.

39.

Jankovic

, Industrial Eng. Chem. Res., 48, (2009), 7044–7053.

Model	Differential form f(α) = (1/k) dα/dt	Integral form g(α) = kt
	Nucleation models
Power law (P2)	2α^(1/2)	α^(1/2)
Power law (P3)	3α^(2/3)	α^(1/3)
Power law (P4)	4α^(3/4)	α^(1/4)
Avarami-Erofeyev (N2)	2(1−α) [−ln(1−α)]^1/2	[−ln(1−α)]^1/2
Avarami-Erofeyev (N3)	3(1−α)[−ln(1−α)]^2/3	[−ln(1−α)]^1/3
Avarami-Erofeyev (N4)	4(1−α)[−ln(1−α)]^3/4	[−ln(1−α)]^1/4
Geometrical contraction models
Contracting area (R2) Contracting volume (R3)	2(1−α)^1/2	[1-(1−α)^1/2]
	3(1−α)^2/3	[1-(1−α)^1/3]
Diffusion models
1-D Diffusion (D1)	1/(2α)	a²
2-D Diffusion (D2)	[−ln(1−α)]⁻¹	[(1−α)ln(1−α)] + α
3-D Diffusion-Jander (D3)	[3(1−α)^2/3]/[2(1−(1−α)^1/3)]	[1-(1−α)^1/3]²
Reaction-order models
First-order (F1)	(1−α)	-ln(1−α)
Second-order (F2)	(1−α)²	(1−α)⁻¹-1

Effect of Cyclo-Olefin Copolymer Loading on Kinetics,Thermodynamics and Model of Linear Low Density Polyethylene Crystallinity

Abstract

Keywords

1 Introduction

2 Experimental

2.1 Materials

2.2 Sample Preparation

Table 1 The formula of the LLDPE/COC blends (wt%) Sample code LLDPE COC A0 100 0 A20 80 20 A40 60 40 A50 50 50 A60 40 60 A80 20 80 A100 0 100

3 Results and Discussion

3.1 Kinetics

References

Table 1
The formula of the LLDPE/COC blends (wt%)

Sample code LLDPE COC

A0 100 0

A20 80 20

A40 60 40

A50 50 50

A60 40 60

A80 20 80

A100 0 100