Induced G phase through intermolecular hydrogen bonding: X. Crystallization kinetics study on two structural isomers

A comparative systematic crystallization kinetics study has been carried out on two distinct novel liquid crystalline isomers, DBA:R:DBA and DBA:H:DBA (where DBA = p-n-decyloxybenzoic acid, R = resorcinol and H = hydroquinone) using differential scanning calorimetry. The kinetics experiment is performed from the crystal G phase (kinetophase), which is a common induced phase in both compounds. The molecular mechanism and dimensionality of crystal growth are studied from the Avrami exponent n while the characteristic crystallization time (t ^*) at each crystallization temperature is deduced from the individual plots of log t vs. Δ H.     

Tetrachlorobisphenol-A adipate polymers. II. Spherulitic crystallization of poly(tetrachlorobisphenol-A adipate)

The spherulitic radical growth rate G of poly(tetrachlorobisphenol-A adipate) was studied at different crystallization temperatures as a function of molecular weight using an optical polarizing microscope. By assuming a two-dimensional growth mechanism, with a jump factor G₀ depending on the molecular weight, and assuming surface energy terms σ_u and σ_e essentially constant, it is possible to correlate the growth-rate data with the model of Hoffman.     

Experimental study of shear-induced crystallization of an impact polypropylene copolymer

The crystallization kinetics of polypropylene was observed during shear and after shear experiments under isothermal condition. The crystallizations were performed in a plate-plate and a fiber pull-out device. The nucleation density, the crystalline growth and the overall kinetics were measured and compared with data obtained in a similar way but during static experiments. The morphologies are spherulitic and formed from nuclei which seem to be randomly distributed. -phase spherulites are always observed but with a nucleation density and a growth rate which depend on shearrate. The nucleation density is strongly enhanced by shear and acts as the main factor on the overall kinetics. The overall kinetics can be analyzed with a two-step Avrami model, where an Avrami exponentn ₁ with a very high value is always observed first after shear and a more usual parametern ₂ for the subsequent crystallization period. This high value ofn ₁ seems to be related to the strong enhancement of nucleation density. The growth rate increases with the shear-rate, but the basic growth mechanisms do not seem to be modified. For crystallizations after shear the growth rate decreases with a long-time delay after shear but not down to the static value. The effect is characteristic of a partial relaxation of chain orientation after shear but with a very unusual time constant.     

Kinetics of mesophase formation and crystallization in poly(diethylsiloxane)

Optical and calorimetric studies of the kinetics of mesophase formation and crystallization in poly(diethylsiloxane) have been conducted. The mesomorphic phase is found to grow from the isotropic melt in the form of lamellar domains about 2 μm thick in the temperature range 293–307 K. According to birefringence data, macromolecules in the mesomorphic lamellae are perpendicular to the end faces. The kinetics of mesophase formation obey the Avrami equation with the morphological parameter n close to 2 (it is equal to 1.75 ± 0.05), which corresponds to the two-dimensional growth of the mesomorphic phase from athermal nuclei. The limiting conversion of the isotropic melt was shown to be temperature-dependent. This is likely to be connected with a change in the number of nuclei with temperature. The crystallization of polymer from the mesomorphic state occurs with retention of the optical texture of the sample. The process proceeds not as a sporadic crystallization of individual mesomorphic lamellae but as a growth of the nucleated crystalline regions via a consecutive incorporation of adjacent crystallizing lamellae.     

Crystallization studies on linear aliphatic n‐polyurethanes

A detailed crystallization study of the linear n‐polyurethane (n‐PUR) family for n ranging from 5 to 12 was carried out by DSC supported by polarizing optical microscopy. The study embraces crystallization of all the n‐PUR under both nonisothermal and isothermal conditions. The odd and even series of n‐PUR defined by the parity of the number of methylenes (n) contained in the polymer repeating unit are considered and separately analyzed. All the members of the two series showed a thermal behavior consistent with their chemical constitution. Isothermal crystallization data were analyzed by the kinetics Avrami approach which revealed that the “crystallizability” of n‐PUR increases steadily with the flexibility of the polyurethane chain. Melting and enthalpy temperatures of isothermally and nonisothermally crystallized n‐PUR were found to vary with n according to a zig‐zag plot characteristic of odd–even effect. Given the structural similitude of n‐PUR with (n + 2)‐nylons, results were referenced to those reported for this family of polyamides. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1368–1380, 2009     

Statistical Theory of Stable and Metastable Transition for Crystallization and Fusion of Homopolymers III Statistical Dynamics of Polymeric Crystallization by Molecular Segregation A General Characteristics for Growth-Rate of Melt-grown Crystals and Their

At first a comprehensive and short review on the characteristics for size growth-rate of crystals is presented. Based on the structural model of micro-nucleus- and crystal-constituent chains and the feature of grown mechanism for crystallization by the molecular segregation of stems, a general principle and method for characteristics of the number growth-rate for micro-crystal-constituent chains and the size growth-rate for crystals by melt-crystallization was proposed. According to the principle, a set of quantitative expressions for the number growth-rate of constituent chains with different sizes and different lengths of segments and the size growth-rate of crystals by four different types of growth with folding, extending, parallel combination of folding and extending and series combination of folding and extending chains was derived by the combination method of statistical mechanics and kinetics. Then four growth-rate equations for the number of constituent chains and the size of crystals produced by four different types of growth are also obtained. These equations can be successful in relating the growth-rate-to the different types of growth and temperature of crystallization and supper-cooling.     

Crystallization of polydioxolan. III. Microscopy and dilatometric analysis of the crystallization kinetics

Crystallization kinetics has been studied for a polydioxolan (PDOL) sample, over a wide temperature range, by dilatometry and microscopy. The dilatometry results can be analyzed using the Avrami equation. At temperatures higher than 22°C, the crystallization data must be analyzed in two steps: the first part of the curve corresponds to PDOL with a very disordered morphology (Phase I) while the second part of the crystallization curve is related to a spherulitic morphology (Phase II). The passage from the low to the high crystallization temperature region is associated with a change in the Avrami exponent from 3 to 4. The crystal surface free-energy product σσ_e was found to be 18 × 10² erg²/cm⁴, very close to that of polyoxymethylene. The crystallization kinetics was studied by microscopy over the temperature range?18 to 35°C. Growth and nucleation rates were recorded. Two phases are found only at temperatures higher than 22°C. The appearance of Phase II is related to a decrease in the growth rate of the sample. From the growth rates, the crystal surface free-energy product σσ_e was found equal to 17 × 10² erg²/cm⁴. The detailed analysis of the crystallization of the two phases reveals a complicated process which can be divided into four different steps: (a) growth of a disordered phase, Phase I; (b) nucleation of a higher birefringence structure; (c) propagation of a high birefringence phase; and (d) spherulitic growth, Phase II. The analysis of PDOL crystallization strongly suggests the presence of a hedrite → oval → spherulite transition: the hedrite formation corresponds to step (a), the oval formation to steps (b) and (c), and the spherulite formation to step (d).     

Isothermal melt and cold crystallization kinetics of poly(aryl ether ketone ether ketone ketone)

The isothermal melt and cold crystallization kinetics of poly(aryl ether ketone ether ketone ketone) are investigated by differential scanning calorimetry over two temperature regions. The Avrami equation describes the primary stage of isothermal crystallization kinetics with the exponent n ≈ 2 for both melt and cold crystallization. With the Hoffman–Weeks method, the equilibrium melting point is estimated to be 406 °C. From the spherulitic growth equation proposed by Hoffman and Lauritzen, the nucleation parameter (K_g) of the isothermal melt and cold crystallization is estimated. In addition, the K_g value of the isothermal melt crystallization is compared to those of the other poly(aryl ether ketone)s. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1992–1997, 2000     

Polymeric nature of selenium crystallization. II. Crystallization kinetics and secondary crystallization

The crystallization of elemental selenium has been studied in light of present concepts of crystallization in organic polymers. Bulk-crystallization kinetic data as measured by a dynamic density technique and spherulite growth-rate data as measured by optical microscopy are presented for the temperature range 70°C to 160°C. Plots of extent of isothermal crystallization versus time were sigmoidal in shape. Spherulite growth rates were constant for a given temperature and reached a maximum at approximately 130°C. Evidence is presented for secondary crystallization in selenium, and a model is proposed for destruction of chain folds with interlamellar crystallization during the spherulitic-to-“metallic” transformation above 100°C.     

Crystallization kinetics study on higher homologues of benzylidene aniline compounds: impact of phase variant on nucleation process

A systematic kinetic study leading to the crystallization process from the kinetophases (which occur prior to crystal phase) smectic B, crystal G and smectic F is performed on representative compounds of the homologous series p -phenylbenzylidene-p′-alkylanilines (PBnA) and p-n -alkoxybenzylidene-p′-alkylanilines (nO.m) these compounds are p-phenylbenzylidene-p′-nonylaniline (PB9A), p -phenylbenzylidene-p′-tetradecylaniline (PB14A), p-n -pentadecyloxybenzylidene p′-tetradecylaniline (15O.14) and p-n -octadecyloxybenzylidene-p′-nonylaniline (18O.9). The molecular mechanism and dimensionality in crystal growth from the kineto phases are computed from the Avrami equation, while the characteristic crystalline time (t ^*) at each crystallization temperature is deduced from the individual plots of log t vs. Δ H. The low magnitudes of the dimensionality parameter n infers the occurrence of diffusion-controlled transformations leading to the formation of plates or needles of finite size possessing impinged edges. The degree of variation in the value of n at each crystallization temperature also reveals the existence of an independent nucleation mechanism for any individual member of the series. The influence of the terminal alkyl chain lengths on the rate of crystallization is determined from a comparative study with the reported analogous compounds.     

Prediction of poly(oxymethylene) non-isothermal crystallization behaviour from isothermal data

The spherulite growth, nucleation-related,K _g, parameter values obtained from isothermal data (by DSC or optical microscopy) and two other adjustable parameters (the spherulite growth rate preexponential factor and the Avrami's or Tobin's exponent,n) have been used with Nakamura's and Tobin's modified non-isothermal equations to model the kinetics of polymer non-isothermal crystallization. Malkin's model was also tested, for comparison. It is shown that, for polymers that crystallize on cooling almost entirely at temperatures higher than the maximum growth rate temperature, this Tobin's-like non-isothermal model accurately describes the experimental behaviour with only 2 parameters.     

Confined crystallization of polymers within anodic aluminum oxide templates

In this article, a review of recent literature on confined crystallization within nanoporous anodic aluminum oxide (AAO) templates is presented. For almost all infiltrated polymeric materials, crystal orientation within the nanopores is a function of pore diameter. T_c and T_m usually decrease and are a function of pore size. When no pore interconnection remains, the crystallization occur at large supercoolings in heterogeneity free environments. Hence, the nucleation mechanism changes from heterogeneous to surface or homogeneous nucleation. The crystallization kinetics of infiltrated polymers should be close to first order, since in confined environments nucleation is the determining step of the overall crystallization and Avrami indexes (n) of ～1 (or lower in some cases) should be obtained. Examples are provided where these conditions have been met and first order kinetics (n = 1) were measured as opposed to higher orders (n = 3?4) for the same polymer in the bulk. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1179–1194     

A distribution kinetics approach for crystallization of polymer blends

The cluster distribution approach is extended to investigate the crystallization kinetics of miscible polymer blends. Mixture effects of polymer-polymer interactions are incorporated into the diffusion coefficient. The melting temperature, activation energy of diffusion, and phase transition enthalpy also depend on the blending fraction and lead to characteristic kinetic behavior of crystallization. The influence of different blending fractions is presented through the time dependence of polymer concentration, number and size of crystals, and crystallinity (in Avrami plots). Computational results indicate how overall crystallization kinetics can be expressed approximately by the Avrami equation. The nucleation rate decreases as the blending fraction of the second polymer component increases. The investigation suggests that blending influences crystal growth rate mainly through the deposition-rate driving force and growth-rate coefficient. The model is further validated by simulating the experimental data for the crystallization of a blend of poly(vinylidenefluoride)[PVDF] and poly(vinyl acetate)[PVAc] at various blending fractions.     

Crystallization kinetics and melting behavior of metallocene short‐chain branched polyethylene fractions

Metallocene polyethylene (mPE) fractions are recognized as being more homogeneous with respect to short‐chain branch (SCB) distribution as compared with unfractionated mPEs. Differential scanning calorimetry and polarized optical microscopy (POM) were used to study the influences of SCB content on the crystallization kinetics, melting behavior, and crystal morphology of four butyl‐branched mPE fractions. The parent mPE of the studied fractions was also investigated for comparative purposes. mPE fractions showed a much simpler crystallization behavior as compared with their parent mPE during the cooling experiments. The Ozawa equation was successfully used to analyze the nonisothermal crystallization kinetics of the fractions. The Ozawa exponent n decreased from about 3.5 to 2 as the temperature declined for each fraction, indicating the crystal‐growth geometry changed from three‐dimensional to two‐dimensional. For isothermal crystallization, the fraction with a lesser SCB content exhibited a higher crystallization temperature (T_c) window. The results from the Avrami equation analysis showed the exponent n values were around 3 (with minor variation), which implied that the crystal‐growth geometry is pseudo‐three‐dimensional. Both of the activation energies for nonisothermal and isothermal crystallization were determined for each fraction with Kissinger and Arrhenius‐type equations, respectively. Double melting peaks were observed for both nonisothermally or isothermally crystallized specimens. The high‐melting peak was confirmed induced via the annealing effect during heating scans. The Hoffman–Weeks plot was inapplicable in obtaining the equilibrium melting temperature (T_m°) for each fraction. The relationship between T_c and T_m for the fractions is approximately T_m = T_c (°C) + 8.3. The POM results indicated that the crystals of parent or fractions formed under cooling conditions did not exhibit the typical spherulitic morphology as a result of the high SCB content. © 2002 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 325–337, 2002     

Thermally activated crystallization of two FeNiPSi alloys

The crystallization kinetics of two alloys in the Fe-Ni-P-Si quaternary system have been investigated, with both isothermal and continuous heating experiments, by means of differential scanning calorimetry. Both alloys present two separated crystallization processes. The Johnson-MehlAvrami-Erofeev equation with a rate constant following the Arrhenius behavior gives the best fit of the experimental data. In all processes the value of its JMAE kinetic exponent is not constant. In the nearly stages, n changes steeply revealing the transient nucleation effect to reach values corresponding to a three-dimensional volume growth controlled by diffusion in the central part (0.3<x<0.55). Latter in the transformation n continuously decreases reflecting the saturation of nucleation. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crystallization in poly(n-octadecyl methacrylate) monolayers

The crystallization kinetics of poly(n-octadecyl methacrylate) has been studied at the air–water interface. The rate of the crystallization has been measured by the decrease in the area of monolayers with time at various temperatures and surface pressures. The crystallization isotherms have been analyzed by the general mathematical treatment of the kinetics of phase changes, and the results show linear growth to be dominant. The variation of the rate constant with temperature and pressure has been illustrated by the difference in the supersaturation defined by introducing the equilibrium pressure-area isotherms.     

NMR approach to the kinetics of polymer crystallization. 1. Cis-1,4-polybutadiene

The isothermal crystallization kinetics of cis-1,4-polybutadiene (PB) in bulk, was studied over the temperature range 193 to 235 K, using ¹H pulsed high-resolution FT-NMR. Analysis of the spectral line area and width, corresponding to the resonance of protons bonded to noncrystalline chain segments, yields two major results:

• (i) The line area variations are associated with the overall progression of crystallization in the sample, which is shown to obey on Avrami law. The time exponent n and rate constant k were determined for each isotherm; their temperature dependence reflects the nucleation and crystal growth mechanisms and provides an estimate of relevant thermodynamic parameters.
• (ii) The line-width is assumed to be closely related to a statistical network with the average mesh size determined by a random distribution of crystallites. Finally, concomitant spin-lattice relaxation time (T₁) measurements show an increase of this parameter which parallels the development of the crystalline fraction.

     

Crystallization kinetics of crosslinkable polymer complexes of novolac resin and poly(ethylene oxide)

Results of a study on the isothermal crystallization and thermal behavior of both uncured and hexamine-cured novolac/poly(ethylene oxide) (PEO) complexes are reported. The crystallization behavior of PEO in complexes is strongly influenced by factors such as composition, crystallization temperature, complexation, and crosslinking. The time dependence of the relative degree of crystallinity at high conversion deviated from the Avrami equation. The cured complexes exhibited an obvious two-stage crystallization (primary crystallization and crystal perfection), and this was more evident at higher crystallization temperature and high PEO-content. The addition of a noncrystallizable component into PEO caused a depression of both the overall crystallization rate and the melting temperature. In general, complexation and curing resulted in an increase in the overall crystallization rate. Complexation and curing are beneficial to the nucleation of PEO. Additionally, curing led to changes of the nucleation mechanism. Experimental data on the overall kinetic rate constant K_n were analyzed by means of the nucleation and crystal growth theory. For uncured complexes, the surface free energy of folding, σ_e, increased with increasing novolac content, whereas for cured complexes, σ_e displayed a maximum with the variation of composition. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2726–2736, 1999     

Kinetics analysis of the isothermal crystallization of Cu55Zr45 metallic glass by differential scanning calorimetry

The crystallization kinetics of Cu₅₅Zr₄₅ (at%) glassy alloy is studied under isothermal condition using differential scanning calorimetry (DSC). The plot of correlation between the crystallized volume fraction α and annealing time t shows a sigmoid-type curve, which is steeper with higher annealing temperature. Furthermore, in isothermal crystallization condition, local activation energy E_α values, determined using the Arrhenius equation, range from 181.1 to 187.8 kJ/mol, which is nearly a constant. The local Avrami exponent n(α) values, obtained by the Johnson-Mehl-Avrami equation, which range from 2.2 to 4.0 at different annealing temeperatures, which indicates that the crystallization mechanism is diffusion-controlled transformation. Moreover, n(α) becomes greater with increasing annealing temperature, which indicates that annealing temperature can affect nucleation rate and growth type.     

Crystal G phase induced through intermolecular hydrogen bonding IV: a study of crystallization kinetics

A systematic crystallization kinetic study using thermal microscopy and differential scanning calorimetry has been carried out on two novel liquid crystalline compounds, DBA:MHB and DBA:ACP. These involve intermolecular hydrogen bonding between 4-n-decyloxybenzoic acid (DBA) and methyl 4-hydroxybenzoate (MHB); and between DBA and 2-amino-5-chloropyridine (ACP). The kinetics experiments were performed from the crystal G phase, which is a common induced kinetophase in both the compounds. Further, the proton donor and acceptor capabilities of the -COOH group of DBA towards the -OH group of MHB and -N atom of ACP were studied in the light of mesomorphism and rate of crystallization. The dimensionality in the crystal growth and the sporadic nucleation were estimated from the Avrami exponent, n. A similar type of crystallization mechanism is predicted to operate for all the crystallization temperatures. The characteristic crystallization time (t?) at each crystallization temperature is deduced from the individual plots of log t vs. ΔH (change in enthalpy).