Theoretical Aspect of Crystallization Temperature at Maximum Crystal Growth Rate

Okui, Norimasa

doi:10.1295/polymj.19.1309

Cited by 20 publications

(10 citation statements)

References 51 publications

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“…For example, the reptation energy is close to 5.5Kcal/mol for n-paraffin [51]. This suggests that the ratio of (∆E/∆H m ) yield about 5.6, which is satisfactory agreement with results for polymers [33]. In metals, ∆E is available experimentally from self-diffusion study both in the melt and in the solid.…”

Section: Ratio Of ∆E and ∆H Msupporting

confidence: 68%

“…The relations for the Arrhenius expression [33] and for WLF expression [18] in the molecular transport term are formulated as follows. For Arrhenius expression in the molecular transport term,…”

Section: Master Curve For Crystal Growth Ratementioning

confidence: 99%

“…On the other hand, high molecular weight polymers exhibit their molecular adsorption with a train-loop conformation (β equals to 0.5) and their molecular movements are controlled with the reptation mode (γ = 1), consequently α yields to −0.5, which may be the case for F CC. For Arrhenius expression in the molecular transport term [33,34],…”

Section: Molecular Weight Dependence Of Maximum Crystal Growth Ratementioning

confidence: 99%

“…It has been well known that a ratio of T cmax /T o m is a nearly constant for a wide variety of materials [31][32][33][34] including metals, inorganic substances, organic compounds and polymers. For example, the ratio of T cmax /T o m for polymeric materials is about 5/6 [33,34]. Constancy of the ratio of T g /T o m is also widely known as BoyerBeaman rule [35,36].…”

Section: Introductionmentioning

confidence: 99%

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Maximum Crystal Growth Rate and Its Corresponding State in Polymeric Materials

Okui

Umemoto

2003

Polymer Crystallization

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Abstract. The temperature dependence of crystal growth rate (G) shows a bell shape with the maximum growth rate G max. The activation energy for the molecular transport in G could be expressed in terms of equation of either Arrhenius or WLF. The G max showed remarkable molecular weight dependence. The plots of G/Gmax against T /Tcmax showed a single master curve without molecular weight dependence. The ratio of Go/Gmax gave a constant value for each polymer. Plots of ln(G/Gmax)/ ln(Go/Gmax) against T /Tcmax for various polymers showed the universal curve. The molecular weight dependence of Gmax was expressed as Gmax ∝ MW α , α was a constant but depending on the morphological features on the crystallization. The value of α was a function of the adsorption mechanism of polymer molecules on the crystal growth front and its diffusion mechanism. The ratio of T cmax/T o m was formulated. Tcmax was also correlated to many other thermodynamic transition temperatures. IntroductionAccording to a classical crystallization theory, a temperature dependence of linear crystal growth rate (G) can be expressed by two exponent factors, such as the molecular transport term (∆E) and the nucleation term (∆F ) [1][2][3]. These two terms have opposing temperature dependence thereby bring about a maximum growth rate (G max ). In fact, many polymeric materials show a bell shape temperature dependence of crystal growth rate, showing the maximum growth rate at T cmax [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. This equation has been applied frequently to data of spherulitic growth rate. Application to the polymer crystallization leads to that the molecular transport term is considerably important in the lower temperature ranges. The transport term can be expressed by either WLF or Arrhenius type. In analyzing the crystallization data in bulk polymers, the WLF expression has been used much familiar than the Arrhenius type, since it has been believed that the former expression fits the data better than the later one. However, the transport term could be sufficiently expressed by the Arrhenius type in polymer crystallization [18][19][20][21]. It is worth to recheck which transport term equation is better describing the temperature dependence of the linear crystal growth rate.On the basis of G max for many crystalline materials, a universal master curve of temperature dependence of crystal growth rate has been proposed by Magill et al. [22,23]. This universal curve comes from a phenomenological basis. The universal master curve is derived from the corresponding state in the growth rate

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Section: Ratio Of ∆E and ∆H Msupporting

confidence: 68%

Section: Master Curve For Crystal Growth Ratementioning

confidence: 99%

Section: Molecular Weight Dependence Of Maximum Crystal Growth Ratementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Maximum Crystal Growth Rate and Its Corresponding State in Polymeric Materials

Okui

Umemoto

2003

Polymer Crystallization

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“…It should be noted that due to the diffusion term, the actual growth rate decreases at low temperatures, resulting in the maximum rate locating around T R ¼ 5=6. 13,14) The rate becomes zero at glass transition temperature, T R ¼ 2=3. We find that the magnetic field accelerates preferentially the growth of the mesophase with a parallel orientation to the field (in the case of a > 0), while the growth rate of the mesophase with a perpendicular orientation is suppressed.…”

Section: Preferential Alignment Modelmentioning

confidence: 99%

Phase Transformation of Polymeric Materials in High Magnetic Field

Kimura

2003

Mater. Trans.

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A model to describe a non-rotation type magnetic alignment of crystalline polymers during crystallization from melts is presented. The model is based on the presence of mesophase existing between the melt phase and the crystalline phase, with an extremely small transformation enthalpy and a resultant large shift of melting point in the presence of a magnetic field. A calculation of the magnetic effect on the nucleation and growth rates of mesophase is carried out. It is shown that these rates are enhanced for the mesophase with a specific orientation with respect to the applied field, resulting in alignment.

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Crystal growth rates and master curves of poly(ethylene succinate) and its copolyesters using a nonisothermal method

Tsai

Chen

et al. 2010

J Polym Sci B Polym Phys

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The spherulitic growth of poly(ethylene succinate) (PES) and two PES‐rich copolyesters at constant cooling rate was monitored and recorded using a system of polarized light microscope. Individual experiment of these polyesters lasted 40, 60, and 120 min, respectively. A continuous curve of isothermal growth rates between the melting and glass transition temperatures can be obtained after curve fitting procedures. These curves fit very well with those data points determined in the isothermal experiments, which are time consuming. The continuous data of PES was analyzed with the Hoffman (Lauritzen equation. A transition of regime II → III was found at 70.7 °C, which is very close to the literature values. The maximum growth rate was formulated in the Arrhenius and WLF expressions for the molecular transport term. A master curve of crystal growth rate for PES was constructed based on the continuous data of PES. When the reduced growth rates after normalization were plotted against the reduced temperatures, a universal master curve was observed for PES and two PES‐rich copolyesters. This nonisothermal method provides an efficient and reliable way for studying the crystallization kinetics of polymer and for constructing a universal master curve of crystal growth rate of PES. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 932–939, 2010

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Theoretical Aspect of Crystallization Temperature at Maximum Crystal Growth Rate

Cited by 20 publications

References 51 publications

Maximum Crystal Growth Rate and Its Corresponding State in Polymeric Materials

Maximum Crystal Growth Rate and Its Corresponding State in Polymeric Materials

Phase Transformation of Polymeric Materials in High Magnetic Field

Crystal growth rates and master curves of poly(ethylene succinate) and its copolyesters using a nonisothermal method

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