Crystallization Rate Constant Research Articles

Eco-friendly zinc-metal-organic framework as a nucleating agent for poly (lactic acid)

Eco-friendly poly(L-lactic acid) (PLA) can be made more versatile, and its crystallization rate is accelerated by adding Zinc-based metal-organic framework (Zn-MOF) particles. Using differential scanning calorimetry (DSC), the non-isothermal melt crystallization behavior of biodegradable PLA nucleated by 0.3 to 3 wt% of Zn-MOF was examined. The non-isothermal melt crystallization kinetics parameters were determined using a modified Avrami model and Mo approach. Zn-MOF dramatically accelerated the crystallization process, as evidenced by several non-isothermal crystallization metrics, including the crystallization half-time and crystallization rate constant. The melt crystallization temperatures of the PLA-Zn-MOF composites, with contents of 0.7 and 1 wt%, were increased by 21 °C compared to the neat PLA. Using the Friedman isoconversional kinetic method, the neat PLA and PLA-Zn-MOF composites' effective activation energy values, ∆E, were determined. The ∆E values of PLA-Zn-MOF from 0.3 to 1 wt% Zn-MOF composites were lower than that of neat PLA. Moreover, polarized optical microscopy revealed the formation of numerous small-sized PLA spherulites upon Zn-MOF addition. The results indicate that the Zn-MOF (at concentrations of 0.7 to 1.0 wt%) can be used as an efficient nucleating agent for PLA, where it increases the melt crystallization temperature, nucleation density, and crystallinity without changing the crystalline structure, while also significantly reduces the effective activation energy and the size of spherulites. Additionally, scanning electron microscopy confirms good dispersion of Zn-MOF (0.3 to 1 wt%) within the PLA matrix.

Non‐isothermal crystallization kinetic of recycled PET and its blends with PBT modified with epoxy‐based multifunctional chain extender

AbstractA fundamental understanding of crystallization behavior is essential for the processing of both virgin and recycled polymers. This research delves into the crystallization characteristics and non‐isothermal crystallization kinetics of recycled polyethylene terephthalate (rPET) and its blends with poly butylene terephthalate (PBT), which have been modified using epoxy‐based multifunctional chain extenders (CE). The preparation of rPET/PBT blends involved a twin‐screw extruder, with varying weight ratios and different CE concentrations. Differential scanning calorimetry was employed to perform crystallization analysis on the samples. The results underscore the profound impact of blend composition on the thermal characteristics of the system, with CE exerting only a marginal influence. The glass transition temperatures (Tg) of the two polymers were measured at 49 and 79°C. During blending, the Tg values demonstrated variations relative to the proportions but did not adhere to the Fox equation. Furthermore, PBT was found to enhance the crystallization tendencies of rPET, resulting in an increase in relative crystallinity from 11% to 36%. Notably, the crystallization rate of PBT at 0.40 min−1 exceeded that of rPET at 0.36 min−1. PBT minimally affected the crystallization rate constant of rPET‐dominant blends, while rPET significantly reduced the crystallization rate in PBT‐dominant blends.

Effects of Mannitol and Xylitol on the Quality of Spicy Wheat Gluten Sticks

The present study sought to evaluate the effects and mechanisms of mannitol and xylitol on the regeneration of spicy wheat gluten sticks (SWGSs) through texture profile analysis (TPA), Fourier-transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), X-ray diffraction (XRD), and low-field nuclear magnetic resonance (LF-NMR). The rate constant of crystallization and the relative degree of crystallinity of SWGS substantially reduced with polyols addition after 4 weeks of storage at 4°C. The peaks near 3385 cm−1 and 1081 cm−1 in FTIR of SWGS became wider with the addition of mannitol and xylitol, indicating that mannitol and xylitol formed hydrogen bonds by binding to wheat starch. The DSC experiment results showed that the addition of mannitol and xylitol could reduce the Tp and ΔH of SWGS powder effectively under different storage times. The NMR results showed that the water in SWGS was mainly immobile water, and the addition of mannitol and xylitol could increase the content of bound water and immobile water in SWGS and reduce the water migration. These results provided deeper insights into the action mechanism of mannitol and xylitol in delaying the quality change of starch products during storage, thereby providing a reference for inhibiting SWGS regeneration. Therefore, it could be inferred that improving the quality of SWGS by adding polyol might have significant application prospects in the food industry.

Effect of calcium pimelate on crystallization kinetics of polyphenylene sulfide

AbstractThe use of nucleating agents (NAs) to accelerate semicrystalline polymers crystallization is a widely recognized technique during processing. However, the commercially available NA for poly(phenylene sulfide) (PPS) has been rather limited. In this work, it is found that calcium pimelate (CaPim), a commercial nucleating agent for isotactic polypropylene, could also accelerate the crystallization process of PPS. The influence of CaPim addition on the crystallization behaviors of PPS was investigated under non‐isothermal and isothermal condition. Upon the addition of 0.3 wt% CaPim, the crystallization peak temperature and the onset crystallization temperature increases by 5.3 and 8.4°C at 10°C/min cooling rate, and the half‐time of crystallization reduces 51% at crystallization temperature of 272°C. Polarized optical observation revealed a substantial enhancement in nucleation due to the presence of CaPim. Avrami equation analysis suggested that the nucleating agent significantly increased the crystallization rate constant without affecting the growth dimension. Moreover, Lauritzen–Hoffman theory analysis indicateed that the addition of CaPim lowers the nucleation energy barrier, contributing to its high‐nucleation efficiency. These findings demonstrate that calcium pimelate holds promise as an effective nucleating agent for PPS.

Effect of rice protein on the gelatinization and retrogradation properties of rice starch

In this study, rice starch (RS) was mixed with varying amounts of rice protein (RP; 0 % to 16 %) to explore the effects of protein on the gelatinization and retrogradation of starch during storage. The increased RP addition decreased the viscosity and gelatinization enthalpy of the mixtures but caused an upward trend in the gelatinization temperature, indicating that protein hampers the process of starch gelatinization. Furthermore, RP addition reduced gel hardness, decreased retrogradation enthalpy and crystallization rate constant, but increased Avrami exponent upon RS retrogradation. RP addition also facilitated the mobility of water molecules, weakened the conversion from bound water to free water in the gels, and moderately increased the uniformity and thickness of gel shape. In summary, RP had a dose-dependent effect on the gelatinization and retrogradation behavior of RS, although the anti-retrogradation concentration effect strongly weakened at protein levels exceeding 12 %. It is noteworthy, that excessive RP addition resulted in disulfide bond formation, which increased gel strength and network structure but reduced the ability of RP to facilitate water molecule mobility and restrict water migration, ultimately reducing its anti-retrogradation capability. This phenomenon can be partially attributed to spontaneous protein-protein interaction caused by excessive protein addition, replacing the starch-protein interaction.

Crystallization behavior of stereoblock polylactide with high sequence regularity structure

AbstractStereoblock polylactide (Sb‐PLA) was prepared via a consecutive method by ring‐opening polymerization and its stereocomplex crystallization behavior was investigated by differential scanning calorimetry (DSC), polarized optical microscopy (POM). The molecular weight, sequence structure of anisotropic segments of Sb‐PLA and crystals structure were characterized by using GPC, 1H NMR, 13C NMR and XRD. The Sb‐PLA with bonding a higher stereoregularity chains prepared by the synthesis route exhibited a higher melting point and uniquely stereocomplex crystallization behavior compared with the Sb‐PLA prepared by commonly reported method. The isothermal crystallization results indicated that the crystallization temperature of Sb‐PLA's increased about 20°C higher than reported Sc‐PLA materials. Moreover, crystallization rate constant (K) and crystallization activation energy (ΔE) expressed by the Arrhenius equation demonstrated that Sb‐PLA presents a higher crystallization rate. The data of isothermal crystallization experiments were analyzed based on Lauritzen–Hoffman (LH) theory, crystallization rate constant (G0), nucleation constant (Kg), fold surface free energy (σe), and folding work (q) were estimated to be 1.5 × 1027 μm/min, 1.2 × 106 K2, 113.0 erg/cm2 and 8.20 × 10−21 J, respectively. These results indicated that Sb‐PLA chains with a higher stereoregularity suggested to be the main factor accounting for the formation unique stereocomplex crystals.

Effect of carrier material on the thermodynamic properties and recrystallization kinetics of andrographolide-solid dispersion

This work investigated the effect of the lipophilic long carbon chain of carrier material on the thermodynamic properties and the recrystallization kinetics of solid dispersion (SD). The thermodynamic properties and recrystallization kinetic parameters of amorphous andrographolide (AG)-PEG8000 laurate (SM12)-SD, AG-PEG8000 palmitate (SM16)-SD and AG-PEG8000 behenate (SM22)-SD were determined and calculated by differential scanning calorimetry combining AGV equation and Avrami equation. From AG-SM12-SD to AG-SM22-SD with the increase of the carbon chain length of carrier material, the glass transition temperature, the maximum relaxation enthalpy and the mean relaxation time of SD increased at first and then decreased; the isothermal crystallization rate constants at different temperatures and non-isothermal crystallization rate constants at different heating rates of SD showed a trend of decreasing at first and then increasing. Increasing the carbon chain length of polyethylene glycol fatty acid ester can improve the space-limiting effect of the carrier material on the AG molecule, but the carbon chain length of carrier was not the longer the better. SM16 had the appropriate spatial scale, which better limited the molecular mobility of AG in SD, so AG-SM16-SD has better thermodynamic stability and recrystallization kinetic stability.

Effects of β-amylase treatment conditions on the gelatinization and retrogradation characteristics of wheat starch

The study aims to investigate the change of gelatinization and retrogradation properties of wheat starch (WS) after β-amylase treatment with different activities and different hydrolysis times, and to determine the relationship between the properties and treatment conditions. The contents of total starch, amylose and amylopectin in enzymatic treated samples were determined, and it was found that β-amylase treatment hydrolyzed the samples and increased the amylopectin content. The rapid viscosity analysis (RVA), differential scanning calorimetry (DSC), X-ray diffraction (XRD) and total texture analysis (TPA) were used for investigation. The gelatinization temperature increased but the overall viscosity including the setback and ΔHg decreased with increasing β-amylase activity or treatment time. Compared with WS, the hardness, ΔHr and recrystallization degree of samples decreased during storage, but the crystal structure still remained A-type. The crystallization rate constants of 10–50 U samples decreased by 25.1–41.9% and 10–50 min samples decreased by 7.6–54.6% according to the Avrami model. It was proved that the crystallization rate and retrogradation rate of the samples were slowed down. The results showed that β-amylase treatment had both short-term and long-term inhibition effects on WS aging and there was a stronger correlation between processing time and effect. And higher β-amylase activity had a stronger inhibition effect under the same hydrolysis time.

Study on inhibition effects and mechanism of wheat starch retrogradation by polyols

Effects and mechanism of polyols (mannitol, isomalt or xylitol) on the retrogradation of wheat starch (WS) were investigated by rapid viscosity analysis (RVA), rheological properties, fourier-transform infrared spectroscopy (FTIR), low-field nuclear magnetic resonance (LF-NMR), texture profile analysis (TPA), differential scanning calorimetry (DSC) and X-ray diffraction (XRD) in this study. A decrease in peak viscosity, trough viscosity, breakdown, final viscosity and setback of WS was observed with addition of polyols. The storage modulus (G′) and the change rate of G′ in the presence of polyols were significantly reduced. The number of hydrogen bonds increased accordingly and polyols in starch gel could combine with more water and reduce water migration. After 4 weeks storage at 4 °C, the hardness, retrogradation enthalpies (△H), crystallization rate constant (k) and relative crystallinity (RC) of WS/polyols were significantly reduced compared with those of the blank. Hence, polyol was promising to be a useful additive to inhibit the retrogradation of wheat starch, which provided a reference for inhibiting the retrogradation of starch-containing food.

Isothermal and Non-Isothermal Crystallization Kinetics of PVDF and PVDF/PMMA Blends

Background: poly(vinylidene fluoride) PVDF and PVDF/PMMA blends have been investigated with a focus on the crystal structure, immiscibility and mechanical properties. However, few reports were found on the crystallization behaviors of PVDF and PVDF/PMMA blends, especially on crystallization kinetics. The article is to report the research on isothermal and nonisothermal crystallization kinetics for PVDF and PVDF/PMMA blends using differential scanning calorimetry (DSC). Results: Besides crystallization temperature and isothermal crystallization activation energy, the Avrami equation exponent of PVDF in blends decreased compared with pure PVDF. The nonisothermal crystallization kinetics of PVDF and PVDF/PMMA (70:30) blends were investigated by Ozawa equation, Jeziorny method and crystallization rate constant (CRC) in detail. The nonisothermal crystallization energy of pure PVDF and its blends were determined by the Kissinger and Vyazovkin’s method. Conclusion: The nucleation and growth mechanism of PVDF in blends changed compared with pure PVDF. The Ozawa equation is not applicable in nonisothermal crystallization kinetics of PVDF and PVDF/PMMA blends. The decreasing of crystallization ability of PVDF in blends were found and confirmed by CRC and the decline of crystallization rate constant in Jeziorny method. Such is opposite to the results of Kissinger’s and Vyazovkin’s method, chances are that these two methods were not used to calculate the nonisothermal crystallization activation energy where the nucleation process was influenced.

Inhibition of Long‐Term Retrogradation of Corn, Potato, and Pea Starches by Borax

AbstractThis work aims to develop a new method for inhibiting the long‐term retrogradation of normal corn starch, waxy corn starch (WCS), potato starch, and pea starch with borax. Differential scanning calorimetry results indicate that adding borax clearly reduces the retrogradation enthalpies of the four starches and decreases the crystallization rate constant. The percentage of retrogradation of WCS combined with 5% borax decreases to 12.06% compared with 69.67% for retrograded WCS without borax after 28 d at 4 °C. Low‐field nuclear magnetic resonance analysis shows that borax remarkably decreases the spin–spin relaxation time of the four starches. The results demonstrate that borax can be used as a new inhibitor and can retard the long‐term retrogradation of starch.

Thermal Stability of Fe82Nb2B14REM2 Amorphous Alloys

We analyze the thermal stability and kinetic parameters of crystallization of Fe82Nb2B14REM2 (REM = Y, Gd, Tb, or Dy) amorphous metallic alloys by the method of differential scanning calorimetry. It is shown that the alloys based on iron crystallize in two stages. We compute the activation energy of both stages of crystallization of amorphous alloys according to the Kissinger, Ozawa, and Augis–Bennett models. The procedure of doping of the Fe84Nb2B14 alloy with rare-earth metals leads to an increase in temperature, in the activation energy of crystallization, and in the frequency factor. The decrease in the crystallization rate constant of alloys caused by doping with rare-earth metals reveals their resistance to temperature treatment.

Impact of the Surface Properties of Cellulose Nanocrystals on the Crystallization Kinetics of Poly(Butylene Succinate)

The hydrophilicity of cellulose nanocrystals (CNCs) is a major challenge for their processing with hydrophobic polymers and matrices. As a result, many surface modifications have been proposed to hydrophobize CNCs. The authors showed in an earlier study that grafting alcohols of different chain lengths onto the surface of CNCs using toluene diisocyanate (TDI) as a linker can systematically hydrophobize CNCs to a water contact angle of up to 120° depending on the alcohol chain length. Then, the hydrophobized CNCs were used to mechanically reinforce poly(butylene succinate) (PBS), which is a hydrophobic polymer. As a result of hydrophobization, PBS/CNCs interfacial adhesion and the composite mechanical properties significantly improved with the increasing CNC contact angle. Continuing on these results, this paper investigates the impact of CNC surface properties on the crystallization behavior of PBS using differential scanning calorimetry (DSC). The results showed that the crystallization temperature of PBS increased from 74.7 °C to up to 86.6 °C as a result of CNC nucleation activity, and its value was proportionally dependent on the contact angle of the CNCs. In agreement, the nucleation activity factor (φ) estimated using Dobreva and Gutzow’s method decreased with the increasing CNC contact angle. Despite the nucleation action of CNCs, the rate constant of PBS crystallization as estimated using the Avrami model decreased in general as a result of a prevailing impeding effect. This decrease was minimized with increasing the contact angle of the CNCs. The impeding effect also increased the average activation energy of crystallization, which was estimated using the Kissinger method. Moreover, the Avrami exponent (n) decreased because of CNC addition, implying a heterogeneous crystallization, which was also apparent in the crystallization thermograms. Overall, the CNC addition facilitated PBS nucleation but retarded its crystallization, and both processes were significantly affected by the surface properties of the CNCs.

Kinetics and morphological characteristics of struvite (MgNH4PO4.6H2O) under the influence of maleic acid.

This work reports a stirred-batch lab crystallization to examine the influence of maleic acid (HO2CCHCHCO2H), and temperatures (30 and 40 °C) on crystallization kinetics and morphology of struvite. The crystallization was followed by measuring the pH change up to 70 min. The pH decreased drastically for the first 5 min of the run, then started to tail off. It was found that the crystallization rate constants range from 1.608 to 6.534 per hour, which agrees with the most published value. Higher maleic acid concentrations resulted in greater growth retardation; the highest retardation was 74.21%, which was achieved for 30 °C with 20.00 ppm maleic acid. SEM imaging of the obtained precipitates showed irregular prismatic morphology, and the associated EDX confirmed that the precipitates were struvite (MgNH4PO4⋅6H2O). As checked through XRD, the crystalline nature of the struvite was further confirmed, and that co-precipitation of struvite with struvite-K was observed. The co-precipitation was the result of K+ adsorption onto the crystal surface. Temperatures had less influence on struvite crystallization. At 40oC and 20.00 ppm the rate constant was 1.332 per hour; whereas at 30oC and 0.00 ppm) the corresponding was 1.776 per hour, indicating the retardation of about 25%. Thus, the temperature effect is only 1/3 of the maleic acid effect. The current findings suggest that the presence of maleic acid can be used to elucidate the mechanism of crystallization as well as the crystalline phase transformation of struvite. In practical terms, maleic acid could be potential as a scale inhibitor.

Effect of process parameters on phase behavior and particle size of aspirin during freeze concentration

The present work investigated effect of process parameters on phase behavior of aspirin (ASP) solution and ASP particle size during freeze concentration. ASP solution (3% w/w in 40% w/w TBA in water) was studied using differential scanning calorimetry (DSC) and cold stage polarized light microscopy (CSPLM) at cooling rates of 0.1, 0.5, 1, 3, 5, 10, 20, and 30 °C/min. Significant reduction in D90 of ASP crystals (from 45.6 µm to 3.0 µm) was observed for ASP crystals in frozen solution with increase in cooling rate. Non-isothermal crystallization kinetics (NITC) of ASP in frozen solution using CSPLM revealed linear increase and an exponential increase in Avrami exponent and crystallization rate constant, respectively. NITC results indicated generation of higher nucleation sites and localized multidimensional crystallization with increase in cooling rate. Moreover, the high degree of supercooling and higher supersaturation achieved with increasing the cooling rate further supported the generation of more nuclei and smaller ASP crystals. Finally, the implication of phase behavior was established using lab scale freeze dryer, where particle size (D90) of 41.8, 14.8, and 7.1 µm was obtained with cooling rate of 1 °C/min, 15 °C/min and quench cooling, respectively. The proposed strategy can be applied for development of lyophilized product that can generate parenteral suspension upon reconstitution.

Effect of rice protein hydrolysates on the short-term and long-term retrogradation of wheat starch

In this study, the effect of rice protein hydrolysate (RPH) on the short-term and long-term retrogradation of wheat starch (WS) was investigated. Among the RPH produced using different proteolytic enzymes (alcalase, papain and protamex), WS incorporated protamex-hydrolyzed rice protein which hydrolyzed for 2 h (PRPH-2) exhibited the lowest gel hardness after storage for 7 and 14 days. Compared with native WS, rapid viscosity analyzer (RVA) analysis showed PRPH-2 addition significantly lowered peak viscosity, breakdown and setback values (P <0.05), whereas it increased pasting temperature of WS. Dynamic viscoelastic measurements indicated the presence of PRPH-2 resulted in a decrease in the storage modulus (G') and an increase in the loss tangent (tan δ). Differential scanning calorimetry (DSC) showed that PRPH-2 significantly decreased the retrogradation enthalpy (P < 0.05), enhanced the Avrami exponent (n), and decreased the crystallization rate constant (k) during 28 days of storage. In addition, low field nuclear magnetic resonance (LF-NMR) results showed that PRPH-2 could promote the mobility of water molecules in WS gel. These findings indicated that PRPH-2 may be used to inhibit the short-term and long-term retrogradation of WS, which can be potently used as a natural additive to improve the quality of wheat products.

Evaluation of Relationship Between Crystallization Structure and Thermal‐Mechanical Performance of PLA with MCC Addition

AbstractPoly(lactic acid) (PLA) biocomposite with 1 wt % microcrystalline cellulose (MCC) addition were prepared by melt‐mixed method using torque rheometer and annealed under different isothermal conditions. The morphology, crystallization behaviors, thermal and dynamic‐mechanical properties were evaluated by techniques of polarized optical microscopy (POM), differential scanning calorimetry (DSC), X‐ray diffraction (XRD) and dynamic mechanical analysis (DMA). Nucleus density, crystallization rate and crystallinity (Xc) of PLA matrix were significantly increased by addition of MCC. It was found that MCC could improve the activity of PLA segments at low crystallization temperature (Tc), and the stability of segments in crystal lattice was also enhanced at high Tc. DSC and XRD analysis supported that MCC contributed to the transformation of α’ form into α form in PLA during annealing. The temperature range in which α crystal form appeared for pure PLA was 125 to 135 °C and it was enlarged from 105 to 145 °C for PLA with MCC addition. The Avrami exponent (n) and crystallization rate constant (k) for MCC/PLA decreased and increased respectively, supporting that the time dimension in nucleation mode was inhibited and crystallization kinetics was improved. MCC/PLA showed an increased stiffness and the highest value of storage modulus (E’) was 52 GPa at Tc of 125 °C, which is basically consistent with the condition of maximum Xc. DMA analysis supported that at high Tc, the addition of MCC greatly increased the crystallization ability of PLA and the elasticity and toughness were also improved.

Supersaturation Potential of Amorphous Active Pharmaceutical Ingredients after Long-Term Storage.

This study explores the effect of physical aging and/or crystallization on the supersaturation potential and crystallization kinetics of amorphous active pharmaceutical ingredients (APIs). Spray-dried, fully amorphous indapamide, metolazone, glibenclamide, hydrocortisone, hydrochlorothiazide, ketoconazole, and sulfathiazole were used as model APIs. The parameters used to assess the supersaturation potential and crystallization kinetics were the maximum supersaturation concentration (Cmax,app), the area under the curve (AUC), and the crystallization rate constant (k). These were compared for freshly spray-dried and aged/crystallized samples. Aged samples were stored at 75% relative humidity for 168 days (6 months) or until they were completely crystallized, whichever came first. The solid-state changes were monitored with differential scanning calorimetry, Raman spectroscopy, and powder X-ray diffraction. Supersaturation potential and crystallization kinetics were investigated using a tenfold supersaturation ratio compared to the thermodynamic solubility using the µDISS Profiler. The physically aged indapamide and metolazone and the minimally crystallized glibenclamide and hydrocortisone did not show significant differences in their Cmax,app and AUC when compared to the freshly spray-dried samples. Ketoconazole, with a crystalline content of 23%, reduced its Cmax,app and AUC by 50%, with Cmax,app being the same as the crystalline solubility. The AUC of aged metolazone, one of the two compounds that remained completely amorphous after storage, significantly improved as the crystallization kinetics significantly decreased. Glibenclamide improved the most in its supersaturation potential from amorphization. The study also revealed that, besides solid-state crystallization during storage, crystallization during dissolution and its corresponding pathway may significantly compromise the supersaturation potential of fully amorphous APIs.

Kinetic Analysis of Freeze-Thaw Stability of Mayonnaise.

Kinetic analysis was used to study the destabilization of mayonnaise by focusing on the fat crystals. Mayonnaise prepared from rapeseed oil and soybean oil was stored at temperatures ranging from −20 to −40 °C. The destabilization kinetic parameters were measured by observing oil separation over time. The destabilization rate constant, kd, increased with decreasing temperature. The highest value of kd was 1.28 × 10−3 min−1 at −40 °C for rapeseed oil mayonnaise (RoM) and the lowest was 1.95 × 10−6 min−1 at −20 °C for soybean oil mayonnaise (SoM). At each temperature, the kd value in RoM was higher than that in SoM. However, the order of destabilization, n, followed no specific pattern. The crystallization rate constant, Kc, and Avrami constant, n, were calculated using microscopic images of the fat crystals. The increase in crystallization kinetic parameters with decreasing temperature revealed changes in crystal behavior. Both the destabilization rate constant, kd, and the crystallization rate constant, Kc, depended on the temperature. This temperature dependency behavior showed a correlation between kd and Kc, suggesting that the destabilization rate depended on the rate of growth of fat crystals during the freeze-thawing of mayonnaise.

The role of a secondary process in polymer crystallization: 4 − Polyethylene revisited

AbstractIt is suggested that the overlap of primary and secondary crystallization is a cause of the repeated observation of non‐integer n values in polymer crystallization. The possibility that two concurrent crystallization processes occurring during the crystallization of polyethylene may account for anomalous fractional values of the Avrami exponent, of no theoretical significance, is reconsidered using data from the classical paper by Banks et al. (Polymer 4: 61 − 74 (1963)) on the kinetics of crystallization of polyethylene fractions which placed emphasis on evaluating the secondary crystallization stage. In general constant n values in excess of that expected for the crystallization mechanisms can readily be interpreted in terms of the additional crystallinity developed by the secondary process and these values increase commensurate with the rate constant of secondary crystallization. Constant n values close to but below n = 4.0 are interpreted as due to the presence of an induction period present in the presence of homogeneous nucleation. It is not possible to separate the effect of incorporating both an induction period, lowering the value of n, and secondary crystallization, raising the value of n, in the kinetic equation. © 2017 Society of Chemical Industry