Nonlinear Hoffman Weeks Research Articles

Investigating the equilibrium melting temperature of linear polyethylene using the non-linear Hoffman-Weeks approach

The melting behavior of three linear polyethylene fractions with number average molecular weights of 11, 29, and 100.5 kg/mol was studied as a function of crystallization time with conventional and ultra-fast calorimetry. The initial melting temperatures of non-thickened lamellae formed under isothermal conditions over a range of crystallization temperatures were analyzed with the non-linear Hoffman-Weeks method to determine the equilibrium melting temperature. Tmeq values of 138.4±0.9°C, 139.7.4±0.9°C, and 140.9±0.8°C were estimated for PE 11K, PE 29K, and PE 100K, respectively, in close agreement with those reported in the literature for the melting of extended-chain crystals or with the Gibbs-Thomson analysis. The Lauritzen-Hoffman theory and the non-linear Hoffman-Weeks treatment were modified to account for the effect of the tilt angle, θ, of the crystallized stems of linear polyethylene on the initial average lamellar thickness. Accuracy of the non-linear Hoffman-Weeks method was examined using initial lamellar thickness, ℓg∗ , data reported for PE 29K in the literature at different crystallization temperatures. The equilibrium melting temperature obtained by the Gibbs-Thomson approach and the C2 value extracted from the ℓg∗vs.1/ΔT plot were similar within the limits of experimental error to those obtained here through the non-linear Hoffman-Weeks method. Using the Huggins equation, the equilibrium melting temperature of an infinitely long linear polyethylene chain is found to be equal to 141.4±0.8°C, the same value proposed by Wunderlich.

Lignin-coated cellulose nanocrystals as promising nucleating agent for poly(lactic acid)

We report the effect of lignin-coated cellulose nanocrystals (L-CNCs) on the crystallization behavior of poly(lactic acid) (PLA). PLA/L-CNC nanocomposites were prepared by melt mixing, and the crystallization behavior of PLA was investigated using differential scanning calorimetry. Isothermal crystallization data were analyzed using Avrami and Lauritzen–Hoffman secondary nucleation theory, while the equilibrium melting temperature was determined using the nonlinear Hoffman–Weeks method. The lignin-coated cellulose nanocrystals acted as a nucleating agent and significantly increased the rate of crystallization and degree of crystallinity of PLA in PLA/L-CNC nanocomposites. The Avrami exponent, n, increased in the presence of L-CNCs, displaying a conversion from lamellar morphology to two-dimensional crystal growth. PLA/L-CNC nanocomposites also gave lower values of the nucleation parameters, $$K_{\text{g}}$$ and σ e, due to a reduction in the activation energy for nucleation.

Study on the Thermal Behaviors and the Morphology in PVP/ PA66 Blends

In this paper, PA 66 were solution blended with poly(vinyl pyrrolidone)(PVP), an amorphous polar polyamide. The thermal behaviors and morphology in the blends of polyamides (PA66)) and PVP were investigated by WAXD, DSC, FT-IR and POM methods. The equilibrium melting temperatures for PA 66 in the blends were estimated based on the linear and non-linear Hoffman-Weeks (LHW and NLHW) extrapolative methods. The interaction mode between PVP and PA66 was investigated by FT-IR spectroscopy.

Isothermal crystallization kinetics of anhydrous sodium acetate nucleated poly(ethylene terephthalate)

AbstractStudies on the isothermal crystallization kinetics of poly(ethylene terephthalate) (PET) nucleated with anhydrous sodium acetate were carried out. The nucleated agent had succeeded in promoting greater rates of crystallization in PET. A study of the melting behavior of the samples revealed that the nucleating agents promoted formation of thinner lamellae. The equilibrium melting temperature (T) of samples was determined using linear and nonlinear Hoffman Weeks procedure. The nonlinear Hoffman Week's procedure was found to be inapplicable in the current study. The Lauritzen‐Hoffman secondary nucleation theory was applied to determine the nucleation parameter (Kg), fold surface energy (σe), and work of chain folding (q). σe and q decreased on addition of nucleating agent. The approximate and exact form of the Lauritzen Z‐test was used to determine the operating regime. The operating regime was found to be primarily regime II for the range of temperatures studied. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010

Dispersion, crystallization kinetics, and parameters of Hoffman–Lauritzen theory of polypropylene and nanoscale calcium carbonate composite

AbstractIsothermal and nonisothermal crystallization of polypropylene (PP)/calcium carbonate (CaCO3) with two particle sizes (250–300 nm and 20–25 nm) were studied by differential scanning calorimeter. Equilibrium melting temperature (T) determined from both linear and nonlinear Hoffman–Weeks relations showed that the composites had a lower T as a result of the CaCO3 particles destroying the crystal of PP. Kinetics of the isothermal and nonisothermal crystallization was described by Avrami equation. For the first time, without the assumption of a constant U* value, Lauritzen–Hoffman parameters (U* and Kg) were evaluated directly by data‐fitting method for isothermal crystallization, and by Vyazovkin's method for nonisothermal crystallization. Kg values obtained were similar with and without the assumption of a constant U*and comparable to those in the literature. Both U* and Kg indicate the dual role the CaCO3 particles as nucleating agents to enhance the crystallization and as obstacles to the chain movement to reduce the crystallization. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers

DSC analysis of isothermal melt-crystallization, glass transition and melting behavior of poly( l-lactide) with different molecular weights

Isothermal melt-crystallization, glass transition and melting behavior of poly( l-lactide) (PLLA) with different molecular weights were investigated by using differential scanning calorimetry. Analysis by Avrami equation showed that crystallization was initiated by heterogeneous nucleation, followed by 3-dimensional growth. The maximum reciprocal half-time of crystallization (1/ t 1/2) was detected at 105 °C. Double endothermic peaks were observed around the glass transition for PLLA with intermediate crystallinities, indicating the coexistence of bulk-like and confined amorphous regions. Double-melting behavior was analyzed and combined with the equilibrium melting temperature evaluation by non-linear Hoffman–Weeks extrapolation, from which a value of 207.6 °C was deduced for PLLA of infinite molecular weight. Lauritzen–Hoffman theory was employed to analyze the crystallization kinetics. Regime II-III transition was found to occur at 120 °C for PLLA of lower molecular weight. The crystal morphology was also examined by scanning electron microscopy through chemical etching method.

Effect of nanoscale fully vulcanized acrylic rubber powders on crystallization of poly(butylene terephthalate): Isothermal crystallization

Poly(butylene terephthalate) (PBT) was blended with nanoscale fully vulcanized acrylic rubber (FVAR) powders in a twin extruder, and the FVAR powders were dispersed well in PBT from scanning electron microscopy (SEM) and transmission electron microscope (TEM) investigation. The isothermal crystallization kinetics of PBT/FVAR blends were investigated by differential scanning calorimeter (DSC) and simulated by Avrami model. Equilibrium melting temperature was estimated by the nonlinear Hoffman–Weeks relation. The active energy (Δ E) and nucleation parameters ( K g) increased with the addition of FVAR, suggesting that FVAR particles hindered the crystallization; however more content FVAR had a lower Δ E and K g because FVAR powders acted as heterogeneous nuclei in the nucleation of crystallization and facilitated the crystallization of PBT. The crystallization ability followed the order: PBT > PBT/FVAR6 > PBT/FVAR3 > PBT/FVAR1 when undercooling was considered.

Isothermal Crystallization of Poly(ethylene-co-glycidyl methacrylate)/Silica Nanocomposites

γ-Aminopropyltriethoxysilane was used to modify nano-size silica particles (A-Silica), and silanation was studied by 29Si and 13C CP MAS NMR. 3 wt % original silica (Silica) and modified silica (A-Silica) particles were blended with poly(ethylene-co-glycidyl mathacrylate) (PEGMA) in a twin screw extruder. The dispersibility of these nanocomposites was examined by transmission electron microscopy. The equilibrium melting temperature was estimated by linear and nonlinear Hoffman–Weeks relations, and the kinetics of isothermal crystallization were described by Avrami, Tobin, Malkin, and Urbanovici–Segal models. The results showed that PEGMA containing the modified nano-silica gave the highest equilibrium melting temperature and slowest isothermal crystallization rate. The above four kinetic models predicted the same ranking order in crystallization rate: PEGMA > PEGMA/Silica > PEGMA/A-Silica.

Influence of molecular characteristics on overall isothermal melt-crystallization behavior and equilibrium melting temperature of syndiotactic polypropylene

Overall isothermal melt-crystallization and subsequent melting behavior of metallocene-catalyzed syndiotactic polypropylene resins of various molecular weights were investigated using differential scanning calorimetry (DSC) technique. Two sets of molecular weight range were synthesized with two different metallocene catalyst systems. The kinetics of the overall isothermal melt-crystallization process was analyzed based on various macrokinetic models, i.e. the Avrami, Malkin and Urbanovici–Segal models. The effective activation energy describing the overall isothermal crystallization process over the crystallization temperature range studied was estimated based on an Arrhenius approximation of the obtained Avrami crystallization rate constants. The equilibrium melting temperature for each of these resins was estimated based on the linear and non-linear Hoffman–Weeks extrapolative methods.

Isothermal melt-crystallization and melting behavior for three linear aromatic polyesters

Isothermal crystallization and subsequent melting behavior for three different types of linear aromatic polyester, namely poly(ethylene terephthalate) (PET), poly(trimethylene terephthalate) (PTT), and poly(butylene terephthalate) (PBT), were investigated (with an emphasis on PTT in comparison with PET and PBT). These polyesters were different in the number of methylene groups (i.e. 2, 3, and 4 for PET, PTT, and PBT, respectively). Isothermal crystallization studies were carried out in a differential scanning calorimeter (DSC) over the crystallization temperature range of 182–208 °C. The wide-angle X-ray diffraction (WAXD) technique was used to obtain information about crystal modification and apparent degree of crystallinity. The kinetics of the crystallization process was assessed by a direct fitting of the experimental data to the Avrami, Tobin, and Malkin macrokinetic models. It was found that the crystallization rates of these polyesters were in the following order: PBT>PTT>PET, and the melting of these polyesters exhibited multiple-melting phenomenon. Lastly, the equilibrium melting temperature for these polyesters was estimated based on the linear and non-linear Hoffman–Weeks (LHW and NLHW) extrapolative methods.

Determination of the equilibrium melting point of the β-form of polypropylene

The melting behavior of the β-form of isotactic polypropylene (β-iPP) was investigated as a function of crystallization time and temperature. Calcium suberate, a selective β-nucleating agent was used to produce samples that consist entirely of β-form i-PP. The experimental melting points were recorded at different crystallization times and were extrapolated to the start of the crystallization process in order to eliminate the effect of lamellar thickening. Using the non-linear Hoffman—Weeks approach to correlate these extrapolated experimental melting temperatures with the corresponding crystallization temperatures, an equilibrium melting point of 209°C was obtained for β-iPP. The equilibrium melting point estimated through the non-linear Hoffman—Weeks analysis is about 30°C higher than that (Tm0=177°C) obtained on the basis of the linear extrapolation. These results are consistent with earlier claims that a linear extrapolation of Tm−Tc data leads to an underestimation of the equilibrium melting point. The results obtained for β-iPP exemplify the importance of accounting for both the isothermal lamellar thickening effects and the non-linearity in the Tm−Tc correlation, when the determination of an equilibrium melting point is carried out using a procedure based on the predictions of the Lauritzen—Hoffman secondary nucleation theory.

Crystallization and melting behavior in syndiotactic polypropylene: Origin of multiple melting phenomenon

AbstractThe melting behavior of syndiotactic polypropylene (s‐PP) after isothermal crystallization from the melt state was studied using differential scanning calorimetry (DSC) and wide‐angle X‐ray diffraction (WAXD) techniques. Three melting endotherms were observed for isothermal crystallization at high degrees of undercooling. The minor endotherm, located closed to the corresponding crystallization temperature, was postulated to be the melting of the secondary crystallites formed at the crystallization temperature. The low‐temperature melting peak was found to be the melting of the primary crystallites formed, and the high‐temperature melting peak was a result of the melting of the crystallites recrystallized during a heating scan. The triple‐melting behavior observed in subsequent melting endotherms of s‐PP was therefore described as contributions from melting of the secondary crystallites and their recrystallization, partial melting of the less stable fraction of the primary crystallites and their recrystallization, melting of the primary crystallites, and remelting of the recrystallized crystallites formed during the heating scan. In addition, determination of the equilibrium melting temperature for this s‐PP resin according to the linear and nonlinear Hoffman–Weeks extrapolations provided values of 143.1 and 185.6°C, respectively. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1083–1097, 2001

Isothermal melt crystallization and melting behaviour of syndiotactic polypropylene

The lamellar morphological information and subsequent melting behaviour of syndiotactic polypropylene (s-PP) samples isothermally crystallized at crystallization temperatures ranging from 30 to 95 °C have been investigated using a combination of wide-angle X-ray diffraction (WAXD), small- angle X-ray scattering (SAXS) and differential scanning calorimetry (DSC) techniques. Three known methods for determining the equilibrium melting temperature Tm °, namely the Gibbs-Thomson extrapolation, the linear Hoffman-Weeks extrapolation and the non-linear Hoffman-Weeks extra- polation, have been employed to evaluate this important thermodynamic parameter, and the results obtained are compared. Finally, an estimate of the equilibrium melting temperature for a perfect s-PP sample (T m °) 100% is given. # 2000 Society of Chemical Industry

Melting temperature depression for low ether content polyether-polyester block copolymers with amide linkages

Melting behavior of a series of polyether-polyester block copolymers with low ether contents was studied. Significant melting-reorganization-remelting was suggested by means of differential scanning calorimetry. The equilibrium melting temperature of the copolymers was obtained by using the Hoffman-Weeks extrapolation. It has been found that the use of the on-set melting temperature for the Hoffman-Weeks plots is less reliable than the use of the corrected peak melting temperature. Copolymerization of polyetheramides with polyesters leads to a significant melting temperature suppression for the polyester crystal. We hypothesize that the locations of the junction points between blocks can be treated as chain ends for the crystallizable polyester blocks: the polyether-polyesters grow to form extended chain-like crystals with lamellar thickness limited by the polyester block length. For comparison, the nonlinear Hoffman-Weeks treatment, recently proposed by Marand, has also been applied to examine the behavior of melting temperature depression. Although the Tmo obtained from nonlinear extrapolation is much higher than the Tmo obtained from the Hoffman-Weeks extrapolation, similar trend regarding the composition dependence of Tmo have been found.