Linear Crystal Growth Research Articles

Melting of polymer single crystals studied by dynamic Monte Carlo simulations

We report dynamic Monte Carlo simulations of lattice polymers melting from a metastable chain-folded lamellar single crystal. The single crystal was raised and then melted in an ultrathin film of polymers wetting on a solid substrate, mimicking the melting observations made by using Atomic Force Microscopy. We observed that the thickness distribution of the single crystal appears quite inhomogeneous and the thickness increases gradually from facetted edges to the center. Therefore, at low melting temperatures, melting stops at a certain crystal thickness, and melting-recrystallization occurs when allowing crystal thickening; at intermediate temperatures, melting maintains the crystal shape and exhibits different speeds in two stages; at high temperatures, fast melting makes a melting hole in the thinnest region, as well as a saw-tooth-like pattern at the crystal edges. In addition, the linear melting rates at low temperatures align on the curve extrapolated from the linear crystal growth rates. The temperature dependence of the melting rates exhibits a regime transition similar to crystal growth. Such kinetic symmetry persists in the melting rates with variable frictional barriers for c -slip diffusion in the crystal as well as with variable chain lengths. Visual inspections revealed highly frequent reversals upon melting of single chains at the wedge-shaped lateral front of the lamellar crystal. We concluded that the melting kinetics is dominated by the reverse process of intramolecular secondary crystal nucleation of polymers.

A molecular insight into the nature of crystallographic mismatches in self-assembled fibrillar networks under non-isothermal crystallization conditions

The lengths of the 12-hydroxystearic acid (12HSA) fibers are influenced by crystallographic mismatches resulting from the incorporation of 12HSA monomers into the crystal lattice in an imperfect manner. On a molecular level, this can be differentiated using synchrotron Fourier transform infrared (FTIR) spectroscopy by monitoring the change in area of the 1700 cm−1 and 3200 cm−1 peaks, corresponding, respectively, to the dimerization of the carboxylic acid groups and hydroxyl non-covalent interactions, during crystallization. The crystallographic mismatch is attributed to a plateau in the apparent rate constant for the dimerization of the carboxylic acid head groups while the hydroxyl interactions linearly increase as a function of cooling rate (ϕ). The rate constant for hydroxyl interactions linearly increases as a function of cooling rate while a plateau is observed for the rate of dimerization at cooling rates between 5 and 7 °C min−1. At cooling rates greater than 5 to 7 °C min−1 12HSA monomers do not effectively dimerize before being incorporated into the crystal lattice causing crystal imperfections impeding linear epitaxial crystal growth and produces branched fibers. At slow cooling rates (i.e., less than 5 to 7 °C min−1), long fibers are produced with a fractal dimension between 0.95 and 1.05 and for rapid cooling rates (i.e., greater than 5 to 7 °C min−1) short branched fibers are produced with a fractal dimension between 1.15 and 1.32.

CdS/CdSSe quantum dots in glass matrix

The compositions containing 55 and 60% of silica have been formulated for preparation of glass filters having sharp cut-off at 475 and 575 nm. To achieve cut-off at these wavelengths, the glasses have been doped with CdS/CdSSe and melted at 1200–1300°C. The glass samples were transparent and pale yellow in colour due to presence of CdS/CdSSe tiny nano crystal (Q-dots). In situ growth of CdS/CdSSe nano crystals imparts the yellow/orange/red colour to these glasses. Optical study shows that as prepared glasses have optical cut-off in the range 350–370 nm. The linear crystal growth of CdS/CdSSe in glasses exhibits red shift in optical cut-off. The optical filter having cut-off at 475 nm can be prepared by doping CdS and cut-off filter of wavelength 575 nm by CdSSe. The TEM results show that the CdS/CdSSe nano crystals (Q-dots) ranging from 2–5 nm are uniformly distributed into the glass matrix.

Crystallization behavior of (GeS2)0.1(Sb2S3)0.9 glass

The crystal growth kinetics of antimony trisulfide in (GeS2)0.1(Sb2S3)0.9 glass has been studied by microscopy and DSC. The linear crystal growth kinetics has been confirmed in the temperature range 492⩽T⩽515K (EG=405±7kJmol−1). The applicability of standard growth models has been assessed. From the crystal growth rate corrected for viscosity plotted as a function of undercooling it has been found that the most probable mechanism is interface controlled 2D nucleated growth. The non-isothermal DSC data, corresponding to the bulk sample, can be described by the Johnson–Mehl–Avrami equation.

Face-by-face growth of sucrose crystals from aqueous solutions in the presence of raffinose—II: Growth morphology and segregation

Raffinose segregation into sucrose crystals is experimentally determined along with the modifications of the quantitative sucrose growth morphology, which are in turn related to the different growth conditions. ( C raff, σ) morphodromes nicely represent the conflict between the supersaturation and the raffinose concentration in the solution on the growth morphology, while the overall segregation rate is nearly proportional to the linear overall crystal growth rate. Chernov and Burton–Prim–Slichter models, checked to fit our k eff and ln ( k eff - 1 - 1 ) coefficients as a function of the supersaturation and of the mean linear overall growth rate, do not allow to know whether the segregation occurs either by a process dominated by surface integration, or by additive transfer dominated by volume diffusion within the boundary layer. The distribution of segregated raffinose strictly depends on the { h k l} growth sectors and doped crystals contain deformed lattice zones, as it comes out from X-ray powder diagrams.

Isothermal crystallization kinetics and spherulitic morphology of poly(4‐hydroxybutyric acid‐alt‐glycolic acid)

AbstractIsothermal crystallization behavior of a new regular polyester constituted by glycolic acid and 4‐hydroxybutyric acid units is studied by means of differential scanning calorimetry and hot‐stage optical microscopy. A wide range of crystallization conditions were experimentally accessible, allowing various morphological features to be observed and accurate estimates made of characteristic growth parameters, including radial growth and nucleation rates. Three‐dimensional spherulitic growth from heterogeneous nuclei is deduced from the Avrami analysis, whereas optical micrographs reveal two different spherulitic textures that agree with the existence of two crystallization regimes. These can be well distinguished from the breaks observed in the Lauritzen and Hoffman plots when the linear crystal growth rate or the overall crystallization rate is considered. Ringed and nonringed spherulites with negative and positive birefringence, respectively, can be obtained depending on crystallization conditions and regimes. The studied polyester shows rather complex melting behavior which is interpreted in terms of a recrystallization process involving the two different kinds of spherulites. This study allows polymorphism to be discounted. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2640–2653, 2007

Crystallization and melting behavior of low molar weight PEO–PPO–PEO triblock copolymers

The crystallization behavior of a series of poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) (PEO–PPO–PEO) triblock copolymers (Pluronics) was investigated using time-resolved small-angle X-ray scattering (SAXS), thermal analysis, and polarized optical microscopy. For comparison, a PEO homopolymer, PEO3K, was also included. Time-resolved SAXS during the crystallization of PEO3K shows a typical “two-step” process, i.e., in the initial stage, a metastable crystal with nonintegral folding (NIF) structure forms first, then, it transforms into integral folding (IF) structures, the IF(0) and the IF(1). In contrast with PEO3K, the PEO–PPO–PEO triblock copolymers show a “one-step” crystallization process, i.e., the PEO blocks crystallize directly into the final state and do not change with time. In thermal analysis, only one major solid–melt transition is observed during isothermal crystallization and subsequent melting for triblock copolymers. In the full temperature range, a linear crystal growth is observed. The crystal growth rates monotonously decrease with crystallization temperatures. Notches or breaks due to the NIF–IF transition as clearly seen for PEO3K cannot be recognized for Pluronics. Based on these results, we conclude that the crystallization of PEO–PPO–PEO triblock copolymers follows a “one-step” process; no metastable structure serving as an intermediate state is formed during the crystallization process within the time scale of the current experiments (<120 min).

Kinetics of crystal growth of Sb 2S 3 in (GeS 2) 0.3(Sb 2S 3) 0.7 glass

The crystal growth kinetics of antimony sulfide in (GeS 2) 0.3(Sb 2S 3) 0.7 glass has been studied by DSC and microscopy. The linear crystal growth kinetics has been observed in the temperature range 271 ⩽ T ⩽ 310 °C ( E G = 288 ± 7 kJ mol −1). In fact the crystal growth takes place in the volume of highly viscous (4 × 10 7 > η > 3 × 10 4 Pa s), supercooled melt. The applicability of standard growth models has been assessed. From the reduced growth rate plot (i.e., growth rate corrected for viscosity) as a function of supercooling we find that the most probable mechanism is interface controlled 2D nucleated growth. The non-isothermal DSC data, corresponding to the bulk sample, can be described by the Johnson–Mehl–Avrami equation that provides a reasonable description of crystallization behavior also for partially crystallized samples. However, further analysis of DSC data reveals that this equation cannot be applied for the powder sample even in isothermal conditions.

Isothermal crystallization behavior of undercooled liquid Pd40Cu30Ni10P20 in terms of crystal growth, overall volume crystallization kinetics and their relation to the viscosity temperature dependence

Abstract The crystallization behavior of undercooled liquid Pd40Cu30Ni10P20 metallic alloy has been studied with the aid of differential scanning calorimetry, optical metallography, and electron microscopy methods. The crystallization occurs as a single-stage process starting preferably on the surface of casting voids in the sample volume and on the outer sample cutting planes. The linear crystal growth velocity of crystallizing cells was measured at several constant temperatures in the range 590–620 K. It is constant at constant temperatures and its temperature dependence is in good agreement with the theoretical concepts of Uhlmann using the temperature dependence of the viscosity of the alloy studied. A differential scanning calorimetry study of isothermal overall volume transformation kinetics of samples pre-annealed at 600K for 600s was carried out at several constant temperatures. The experimental data are interpreted on the basis of the equation of Kolmogorov-Avrami-Johnson-Mehl for the case of three-dimensional growth of a fixed number of pre-existing nuclei. The possibility to re-vitrify the crystallized samples by their melting in differential scanning calorimeter, followed by quick cooling with cooling rate of 5Ks−1 is shown. The volume transformation kinetics of revitrified samples has been also studied.

Power law and scaling for molecular weight dependence of crystal growth rate in polymeric materials

The molecular weight (M) dependence of the linear crystal growth rate (G) and the influence of the super-cooling on the relationship between M and G were studied. The molecular weight dependence of G has been expressed generally as G∝Mα at a given super-cooling. The temperature dependence of G shows a bell shape with the maximum growth rate (Gmax). The value of α was −0.5 at the temperature (Tcmax) of Gmax. However, the small super-cooling and the small molecular weight gave a large negative value of α. In other words, the value of α was dependent not only on the degree of super-cooling (ΔT) but also on the molecular weight. The effect on α by these two factors (ΔT and M) goes off to zero at Tcmax and α yields to −0.5. Gmax can be defined as a characteristic intrinsic value to the crystal growth behavior. The molecular weight dependence of Gmax was scaled and expressed as a −0.5 power to molecular weight for all crystalline polymers.

Kinetics of crystal growth of germanium disulfide in Ge0.38S0.62 chalcogenide glass

The crystal growth kinetics of GeS2 in Ge0.38S0.62 glass has been studied by Differential Scanning Calorimetry (DSC) and microsopy. The linear crystal growth kinetics of both high temperature α-GeS2 and low temperature β-GeS2 polymorphs has been observed over a relatively broad range of temperatures, i.e. 420<T<494°C that correspond to viscosity of supercooled melt: 3×109>η>8×105 Pas. It seems that 2D nucleated growth is the most probable mechanism of crystallization for high temperature α-GeS2 under these conditions. However, there are significant deviations for this model for the crystallization of low-temperature β-GeS2. This might indicate some changes in crystal-melt interfacial energy or break down of Stokes–Einstein relation in that particular case. At temperatures below 500°C the temperature range of directly observed crystal growth overlaps with isothermal DSC measurements. In this case overall crystallization kinetics can be described by the Johnson–Mehl–Avrami (JMA) nucleation-growth model for kinetic exponent n≅4. The value of activation energy of nucleation estimated from these experiments EN=434 kJmol−1 is comparable with the activation energy of viscous flow in supercooled Ge0.38S0.62 melt (Eη=478 kJmol−1). A more complex eutectic crystallization involving both GeS2 and GeS phases has been observed at higher temperatures. This process is probably associated with secondary nucleation and cannot be described by a simple JMA model.

Determination of crystallization kinetics in solution

A mathematical model for the calculation of the linear crystal growth rate in solution crystallization was developed, using transient crystal size distribution (CSD) data, the solution concentration curve, and the suspension density of a batch crystallization process without taking in to the secondary processes. Although this method is developed based on a cooling crystallization system, it can be easily extended to other systems e.g., dilution crystallization, precipitation crystallization, etc. An advantage of this method is that crystal shape factors do not affect the linear crystal growth rate. The example of ciprofloxacin hydrochloride crystallization is employed to illustrate this method. The results from this study shows that the model gives more reliable kinetics than alternative methods and the convergence of the model can be easily achieved.

In Situ Ultrasonic Spectroscopy Study of the Nucleation and Growth of Copper Sulfate Pentahydrate Batch Crystallized from Supersaturated Aqueous Solutions

In situ ultrasonic attenuation spectroscopy is applied to the challenging case of monitoring the nucleation and growth of copper sulfate pentahydrate crystallized from supersaturated aqueous solutions, a system not readily amenable to analysis via optical methods due to the intense blue color of the saturated crystallizing solution. In experiments in the 2.8-L rectilinear reactor of a spectrometer, crystallization and dissolution points are reliably detected from the measured attenuation spectra. There are minor differences between data taken at 10 and 50 MHz, notably the lower frequency data appearing to be more sensitive to the particle formation/dissolution process. The nucleation data reveal that the material crystallizes fairly easily as characterized by a metastable zone width of ca. 3-4 °C and a significantly cooling-rate-dependent nucleation order of reaction of ca. 1.7 reflecting the fact that for high cooling rates the nucleation rate is less than that associated with supersaturation generation. The evolving crystal size distribution following nucleation, calculated from ultrasonic attenuation spectroscopy measurements, reveals well-defined oscillations in the observed crystal sizes consistent with the break-up of crystals larger than ca. 250 μm in this crystallizer. From dynamic measurements of changing particle size and concentration during the crystallization process, apparent crystal mass growth rates are calculated to be between 2.3 x 10 -3 kg/m 2 .s at the maximum cooling rate of 0.55 °C/min and 2.02 x 10 -4 kg/m 2 .s at the minimum cooling rate of 0.2 °C/min. On the basis of these data and assuming a spherical particle model, the linear crystal growth rates are estimated to be between 2.0 x 10 -6 m/s at the maximum cooling rate of 0.55 °C/min and 1.8 x 10 -7 m/s at the minimum cooling rate of 0.2 °C/min.

Miscible blends of syndiotactic polystyrene and atactic polystyrene. Part 2. Depolarized light scattering studies and crystal growth rates

Crystallization kinetics and morphology in miscible blends of syndiotactic polystyrene (sPS) and atactic postyrene (aPS) have been investigated by means of time-resolved depolarized light scattering (DPLS), polarized optical microscopy (POM) and scanning electron microscopy (SEM). Two different weight-average molecular weight of aPS, i.e. M w=100k and 4.3k, were used to prepare the blends and denoted sPS/aPS(H) and sPS/aPS(M), respectively. Owing to a dilution effect, addition of aPS reduces the crystal growth rate and the overall crystallization rate of sPS; the reduction is more significant in sPS/aPS(M) of which a depression of equilibrium melting temperature is found due to the enhanced mixing entropy. Linear crystal growth is always observed in sPS/aPS(H) at the temperatures studied (240–269 °C) and results in an interfibrillar segregation morphology revealed by SEM, whereas sPS/aPS(M) with high aPS content exhibits non-linear growth behavior at low supercooling and gives an interspherulitic segregation morphology. Based on the Lauritzen–Hoffman theory, the fold surface free energies ( σ e) of sPS lamellae derived from DPLS and POM are in fair agreement, being 15.1 erg/cm 2 from the former and 12.6 erg/cm 2 from the latter. The peculiarly low values of σ e and the derived work of chain folding are discussed briefly. On addition of aPS, the lateral surface free energy of lamellae remains intact (9.9 erg/cm 2) regardless of aPS molecular weight used, which is ascribed to the absence of specific interaction between sPS and aPS components. Moreover, it seems that the activation energy for sPS chains to diffuse from the miscible melt to the crystal growth front is slightly increased in sPS/aPS(M), plausibly attributable to the extra energy required for the demixing process.

Some observations on the preparation and properties of colloidal silicalites. Part I: synthesis of colloidal silicalite-1 and titanosilicalite-1 (TS-1)

Possible methods for the preparation of colloidal zeolite sols are discussed: direct synthesis is at present the only practicable procedure. The linear crystal growth rate for colloidal TS-1 (≈2.5 at.% Ti) at 175 °C was estimated to be ⩽80 nm h −1, which is lower than that for colloidal silicalite by at least a factor of 3. The introduction of titanium also caused a reduction in the number of crystals nucleated. These effects are ascribed to the difficulty of incorporating the heteroelement into the lattice. No evidence for Ostwald ripening in colloidal silicalite synthesis was found, even at long reaction times. In seeded growth experiments at 100 °C, (i) TPA-silicalite-1 product crystal size could be closely controlled by the quantity of 43 nm seed added, and (ii) crystal linear growth rates in thermally and microwave heated reactions were the same within experimental error. Ageing the precursor sols at 22 °C before crystallisation at 90–175 °C (microwave or thermal heating) demonstrated the generation of proto-nuclei during the room-temperature ageing process. On subsequent heating, these mature into viable nuclei and grow into crystals. An interpretation of this behaviour establishes the relationship of the present results to those of other workers. This identifies the generation of nuclei with a series of chemical steps which lead from the initial equilibration reactions to the formation of the primary replicating unit.

Role of Polymorphous Metastability in Crystal Formation Kinetics of 2,3,6,7,10,11-Hexa(4‘-Octyloxybenzoyloxy)-Triphenylene Discotic Molecules

Phase transition behaviors of a discotic liquid crystal 2,3,6,7,10,11-hexa(4‘-octyloxybenzoyloxy)-triphenylene (HOBT-C8) were investigated. Four phases having different orders and symmetries existed in this system: a discotic nematic phase, a rectangular columnar (ColR) phase, an orthorhombic crystalline (CrI) phase developed upon cooling, and a monoclinic crystalline (CrII) phase formed during heating (Tang, B. Y., et al. Mater. Chem. 2001, 13, 78). The CrI phase represented a metastable phase compared to the CrII phase. On the basis of the results of differential scanning calorimetry, wide-angle X-ray diffraction, and polarized light microscopy (PLM) experiments, three crystallization-temperature (Tc) regions were identified to help study the crystallization kinetics of the CrI and CrII phases. In the large Tc region below 114 °C (region III), the CrI phase formed first despite its metastable nature (monotropic) due to the faster crystallization kinetics of the ColR → CrI phase in this region. The CrI → CrII phase transformation then followed. However, when the Tc ≥ 115 °C in region I, which was close to the melting temperature (Tm) of the CrI phase (Tm = 121 °C), only the CrII phase formed directly from the ColR phase. In the narrow Tc region II where 114 °C ≤ Tc < 115 °C, primary nucleation and overall crystallization rates of CrI and CrII phases were reversed. Linear crystal growth rate measurements in PLM revealed that a minimum in the CrII phase growth rate was found in region II. This indicated that as long as the growth rates of both phases were similar and on the same growth front, the CrII phase formation could be hampered by the growth of the metastable CrI phase.

Crystallization of Poly(Ethylene Oxide) in Thin Films

Crystallization of poly(ethylene oxide) (PEO) in thin films was studied using hot-stage polarized optical microscopy. Isothermal linear crystal growth rates were measured for various film thicknesses at various degrees of undercooling. At a given crystallization temperature, the linear crystal growth rate decreased exponentially with decreasing film thickness below a film thickness of 80 nm. Films showed similar spherulitic morphology down to a film thickness of 30 nm. Control experiments on hydrophilic and hydrophobic surfaces showed that surface chemistry affects stability of the polymer films and causes a competition between crystallization and dewetting.

In Situ Ultrasonic Attenuation Spectroscopic Study of the Dynamic Evolution of Particle Size during Solution-Phase Crystallization of Urea

In situ ultrasonic attenuation spectroscopy is used to examine the batch crystallization of urea from supersaturated aqueous and methanolic solutions. Benchmarking studies carried out on three cases are presented: noncrystallizing milled urea crystals in sunflower oil suspension, crystallizing pure urea from aqueous solution, and crystallizing urea in the presence of biuret habit modifier from methanol solution. In all cases, the technique was found to be capable of monitoring the size and concentration of anisotropic urea particles and it was responsive to the length and width of the needle-shaped crystals up to its upper size limit of 1000 μm. From measurements of changing particle size and concentration during crystallization, mass and linear crystal growth rates were calculated.

Phase identifications and monotropic transition behaviors in a thermotropic main-chain liquid crystalline polyether

A thermotropic liquid crystalline (LC) polyether was synthesized by condensation polymerization of 1-(4-hydroxyphenyl-2-(2-methyl-4-hydroxypheyl)ethane) and α,ω-dibromononane, and abbreviated as MBPE-9. Multiple phase transitions were found via differential scanning calorimetry (DSC) upon heating and cooling. Based on wide-angle X-ray diffraction (WAXD) and polarized light microscopy (PLM) experiments, two monotropic LC nematic (N) and smectic phases and three crystalline (orthorhombic K 1, triclinic K 2 and triclinic K 3) phases were identified. A study on kinetics showed that only when the N phase formation rate was faster than the crystallization rate of K 1 phase which directly grew from the melt, the presence of the N phase could accelerate both the overall crystallization and the linear crystal growth rates of K 1 phase. In a narrow temperature region, two distinct crystal growth rates could be observed: one was directly from the isotropic melt, and another was from the N phase.

MOLECULAR WEIGHT DEPENDENCE OF CRYSTAL GROWTH RATE AND ITS DEGREE OF SUPERCOOLING EFFECT

The molecular weight (MW) dependence of the linear crystal growth rate (G) and the influence of the supercooling on the relationship between MW and G at a given supercooling were studied for poly(ethylene succinate). The spherulite growth rate was measured over a wide range of temperature. It had a bell-shape with a maximum growth rate (G max) that showed a remarkable MW dependence. The MW dependence of G max was mainly a consequence of the MW dependence of G o (pre-exponential factor of the crystal growth rate). The G max increased first with MW up to 3000 and then decreased. The maximum of G max at 3000 was attributed to the transition from extended chain crystallization (ECC) to folded chain crystallization (FCC). The MW dependence of G max was expressed as α was a constant depending on the morphological features of the crystallization. The value of α was nearly unity for ECC below MW of 3000 and α was about −0.5 for FCC above MW of 3000. However, the value of α was strongly dependent on the degree of supercooling when G was plotted against MW at a given supercooling; less supercooling gave a large value of α. The value of α is a function of the adsorption mechanism of polymer molecules on the crystal growth front and its diffusion mechanism. These molecular mechanisms are discussed in this article.