Hoffman-Weeks Extrapolation Research Articles

Dynamic interactions between poly(3-hexylthiophene) and single-walled carbon nanotubes in marginal solvent.

Interfacial interactions between conjugated polymers and carbon nanotubes are pivotal in determining the device performance of nanotube-based polymer electronic devices. Here, we report on interfacial structures and crystallization kinetics of poly(3-hexylthiophene) (P3HT) in the presence of single-walled carbon nanotubes (SWNTs) in anisole by means of transmission electron microscope (TEM) and ultraviolet-visible (UV-vis) absorption spectroscopy. Confined on SWNT surfaces, the P3HT forms nanofibril crystals perpendicular to the long axis of SWNTs. The equilibrium dissolution temperature of the P3HT crystals in anisole is determined to be 381 ± 10 K according to the Hoffman-Weeks extrapolation approach. Upon cooling, the polymer solution spontaneously undergoes a time-dependent chromism. Various kinetics factors such as crystallization temperature, concentration, and SWNT loading have been investigated. It is found that the growth rate (G) of the crystals scales with concentration (C) as G ∝ C(1.70±0.16). The Avrami model is utilized to analyze the nucleation mechanism and the Avrami exponents vary between 1.0 and 1.3. The Lauritzen-Hoffman theory is applied to study the chain-folding process. The fold surface free energy is calculated to be (5.28-11.9) × 10(-2) J m(-2). It is evident that the addition of 0.30 wt % SWNTs reduces the fold surface free energy by 55.6%.

Crystallization and melting of propylene–ethylene random copolymers. Homogeneous nucleation and β-nucleating agents

The different crystallization behavior of two propylene–ethylene random copolymers, (PP-R and PP-RCT), one of which (PP-RCT) contains a β-nucleating agent is investigated in the present paper. Isothermal and non-isothermal crystallization behavior was thoroughly studied. The subsequent melting behavior after isothermal crystallization was studied by means of standard and Step-Scan DSC. The equilibrium melting point of α crystals determined using the Hoffman–Weeks extrapolation was 11.8°C higher than that for β crystals. The Lauritzen–Hoffman theory was applied and the nucleation constant Kg and the surface free energy σe was calculated. From the isothermal experiments it was concluded that the nucleating agent increased drastically the crystallization rate of the copolymer, also promoting the generation of β crystals. On cooling PP-RCT crystallized at about 8°C higher temperatures than PP-R. The non-isothermal crystallization of the materials was examined and for the kinetics analysis the Avrami, Ozawa and Mo models were elaborated. Nucleation activity was calculated with the use of Dobreva’s method. The effective activation energy was calculated for both polymers according to the iso-conversional method of Friedman and lower values resulted as expected in case of the PP copolymer with nucleating agent.

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.

Isothermal crystallization of intercalated and exfoliated polyethylene/montmorillonite nanocomposites prepared by in situ polymerization

Polyethylene/montmorillonite (PE/MMT) nanocomposites with different dispersion states of MMT were prepared by in situ polymerization. Isothermal crystallization of the intercalated nanocomposite, in which the PE chains were confined in the MMT layers, was studied and was compared with that of the exfoliated nanocomposite. It is observed that the intercalated sample has longer induction period, longer crystallization half time and larger crystallization activation energy than the exfoliated sample, showing that crystallization of PE is retarded due to confinement of the MMT layers. Analysis of crystallization kinetics shows that Avrami exponent ( n) increases gradually with crystallization temperature. However, the maximal value of n is 2.0 for the intercalated sample, but it can reach 3.0 for the exfoliated sample. It is inferred that the stems of the PE crystals confined in the MMT layers are parallel to the MMT layers. The Hoffman–Weeks extrapolation method cannot be applied in the intercalated sample because of the small lateral surface of the PE crystals. Based on the depression of the melting temperature, the specific free energy of the PE/MMT interface was estimated, which is about 1.0 mJ/cm 2, much smaller than the free energy of the lateral surface of PE crystals. This is attributed to the origin of the strong nucleation effect of MMT.

Thermodynamic Behavior of Poly(3-alkyl Thiophene) Blends: Equilibrium Cocrystal Formation and Phase Segregation

The equilibrium cocrystal formation of poly(3-alkyl thiophene) (P3AT) blends has been studied by isothermal cocrystallization in a differential scanning calorimeter (DSC-7). The equilibrium melting points (T(m)0) of the cocrystals are measured using the Hoffman-Weeks extrapolation procedure. The equilibrium phase diagrams are of three different types: (a) concave upward, (b) linear, and (c) linear with phase separation at higher content of lower melting component. The phase diagram nature depends on the regioregularity difference and also on the difference in the number of carbon atoms in the pendent alkyl group of the components. The origin of biphasic nature of type "c" phase diagram has been explored from the glass transition temperature (Tg) measurement using a dynamic mechanical analyzer. The biphasic compositions show two glass transition temperatures (Tg) as well as two beta transition temperatures (T beta). The T(g)s of phase-separated regions correspond to almost the component values but the T(beta)s correspond to that of a lower (T beta) component value, and the other is higher than that of the higher (T beta) component value. Possible reasons are discussed from the interchain lamella thickness in the P3AT blends and molecular modeling using molecular mechanics program.

Isothermal crystallization of metallocene-based propylene/?-olefin copolymers

Isothermal crystallization and subsequent melting behavior of two propylene/hexene-1 copolymers and two propylene/octene-1 copolymers prepared with metallocene catalyst were investigated. It is found that γ-modification is predominant in all copolymers. The Avrami exponent shows a weak dependency on comonomer content and comonomer type. At higher crystallization temperatures (Tc) the crystallization rate constant changes more rapidly with Tc and the crystallization half-time substantially increases. Double melting peaks were also observed at high Tc, which is attributed to the inhomogeneous distribution of comonomer units along the polymer chains and the existence of crystals with different lamellar thicknesses. The equilibrium melting temperatures (T) of the copolymers were obtained by Hoffman–Weeks extrapolation. It was found that the T decreases with increasing comonomer content, but are independent of comonomer type, implying that comonomer units are excluded from the crystal lattice. Dilation of the crystal lattice was also observed, which depends on crystallization, comonomer content, and comonomer type. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 240–247, 2005

Melting and crystallization behavior of poly(vinylidene fluoride) produced isothermally in the intercrystalline spaces of poly(ethylene terephthalate) from its blends

AbstractThe melting of isothermally crystallized poly(vinylidene fluoride) (PVF2), produced in the intercrystalline spaces of poly(ethylene terephthalate) (PET) from its blends, showed a unique behavior: the melting temperature decreased with the increasing crystallinity of PVF2 (i.e., with increasing crystallization time) for PVF2 volume fractions of 0.64 and 0.51. The melting temperature of already crystallized PET also decreased as the PVF2 crystallization progressed and the isothermal crystallization temperature of PVF2 increased. Separate reasons were proposed to account for these behaviors. The equilibrium melting temperatures of PVF2 in the blends, measured by the Hoffman–Weeks extrapolation procedure, were used to calculate the polymer–polymer interaction parameter (χ21); only the noncrystallized portion of PET contributing to the mixed amorphous phase was considered. The χ21value (−1.75) was lower than χ12 (−0.14), calculated from the melting temperature depression of PET. However, when they were normalized to the unit volumes of the respective components, the two values were found to be the same. The crystallization rate of PVF2 decreased with an increasing volume fraction of PET in the blend. The Avrami exponent increased for the volume fraction of PVF2 (0.77) and then progressively decreased with an increasing volume fraction of PET. A gradual change in the nature of the regime transition from regime II/regime I to regime III/regime II with increasing PET concentration was observed. The value of the chain‐extension factor of PVF2 significantly increased with an increase in the PET concentration in the blends. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2215–2227, 2004

Crystallization mechanism of regioregular poly(3‐alkyl thiophene)s

AbstractThe crystallization properties of three regioregular poly(3‐alkyl thiophene)s (P3ATs) are studied: poly(3‐hexyl thiophene) (P3HT), poly(3‐octyl thiophene) (P3OT), and poly(3‐dodecyl thiophene) (P3DDT). The morphology of the isothermally crystallized samples is a whisker type. The values of the enthalpy of fusion of ideal crystals (ΔH), determined from the melting point depression in the polymer–diluent system, are 99, 73.6, and 52 J/g for P3HT, P3OT, and P3DDT, respectively. The values of the equilibrium melting point (T), determined from the Hoffman–Weeks extrapolation procedure, are 300, 230, and 180 °C for P3HT, P3OT, and P3DDT, respectively. From the linear extrapolation of the P3AT data, the T and ΔH values of unsubstituted polythiophene are predicted to be 400 °C and 139 J/g, respectively. The crystallization kinetics of these polymers are studied with differential scanning calorimetry, and the Avrami exponents vary between 0.6 and 1.4, indicating one‐dimensional heterogeneous nucleation with linear growth. As the P3AT whiskers are produced from the chain‐folding process, the Lauritzen–Hoffman growth rate theory is applied to analyze the temperature coefficient of the crystallization rate data. Graphical plots indicate a transition from regime I to regime II during isothermal crystallization for all the P3ATs studied. The fold surface energy and the work of chain folding calculated from the slopes of the graphical plots decrease with an increase in the number of carbon atoms of the side chain. The primary crystallization process of the side‐chain crystallization is very fast and is attributed to the zipping effect of the main‐chain crystals. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2073–2085, 2002

Thermal characterization of polycarbonate/polycaprolactone blends

In this work, we prepared blends of bisphenol A polycarbonate (PC) and poly(∈-caprolactone) (PCL) in a wide composition range by melt mixing and solution mixing. Two different molecular weights of PCL were used (nominally, 10.000 g/mol, PCL10, and 80.000 g/mol, PCL80). The thermal behavior of both systems was studied via differential scanning calorimetry under dynamic and isothermal conditions. The blends were miscible in the entire composition range in the liquid and amorphous states, as indicated by the single glass-transition temperature (T g ) exhibited by both the PC/PCL10 and PC/PCL80 blends. The compositional variation of the T g was accurately described by the Fox equation for the PC/PCL80 blends, whereas slight deviations from this equation were exhibited by the PC/PCL10 blends. For blend compositions containing 40% or more PCL, either one or both blend components crystallized. Crystallization occurred during cooling from the melt or during subsequent heating in the form of cold crystallization. Although PCL crystallization was reduced and its crystallization rate decreased with the addition of PC, PCL was a very effective macromolecular plasticizer for PC, to the extent that crystallization during the scan was detected for some blend compositions. Isothermal crystallization experiments allowed the determination of equilibrium melting points (T o m ) by the Hoffman-Weeks extrapolation method. A T o m depression was found for both PCL and PC components as the content of the other blend component was increased. The Avrami equation was closely obeyed by both blend components during the isothermal overall crystallization kinetics up to crystalline conversion degrees of 60-70% and with values of Avrami indices ranging from 3 to 4, depending on the crystallization temperature employed.

Crystallisation and morphology of poly( p ‐dioxanone)

The crystallisation and spherulitic morphology of poly(p-dioxanone) (PPDX), a thermoplastic polyester-ether used for medical applications have been studied. Polarised Optical Microscopy (PM) revealed that isothermally crystallised PPDX exhibits large double banded spherulites with a mean banding spacing that increases as the crystallisation temperature increases. The lack of resolution of optical microscopy prevents the double banding from being clearly observed at crystallisation temperatures below 75°C. The spherulitic morphology changed somewhat as a function of crystallisation temperature from well developed structures with a very clear Maltese cross to spherulites with a more granular texture. A Regime III to Regime II transition in growth was detected according to the Lauritzen and Hoffman analysis of spherulitic growth rate data even though there were no apparent major morphological changes in spherulitic structure as crystallisation temperature was varied apart from that described above. The equilibrium melting point was determined using the Hoffman-Weeks extrapolation procedure and found to be 127°C. Avrami theory was applied to caloriometric overall crystalline conversion data and good fits were obtained with exponents ranging from 3 to 4 as isothermal crystallisation temperature was increased from 50 to 100°C indicating a change from instantaneous to sporadic spherulitic nucleation that was consistent with PM observations. PPDX exhibited a marked tendency to undergo partial fusion and recrystallisation during DSC heating scans. Self-nucleation results evidenced the existence of the usual three self-nucleation domains depending on the self-nucleation temperature (T s ) employed. Additionally, the complex behaviour upon cooling from T s and subsequent melting was studied in detail.

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

Studies on metallocene catalyzed copolymers of ethylene with 10- undecen- 1- ol

Ethylene was copolymerized with 10-undecen-1- ol in the presence of four different metallocene catalyst systems. The copolymers were characterized by differential scanning calorimeter (DSC) and by dynamic mechanical analysis (DMA). It was demonstrated that properties of the catalysts used affected the crystallization behaviour of the copolymers because the catalysts exhibited differences in conversions of the polar comonomer. The step crystallization technique using DSC provided useful information about the differences in comonomer incorporation in the chain. The formation of multiple peaks, based on differences in ethylene sequence length, is much weaker for the copolymers produced with a non- bridged metallocene, than for polymers produced with bridged catalysts. A study of the crystallization rates in nonisothermal experiments exhibited a small decrease in crystallization temperatures with increasing branching. The Hoffman-Weeks extrapolation of melting point vs crystallization temperature gave reasonable results for silylene-bridged copolymers. In DMA, study was made of the storage modulus as an indicator of stiffness and loss tangent as a measure of the effect of branching on the β-relaxations. The DMA measurements indicated a slight increase in the flexural modulus, or stiffness values, of the copolymers relative to the corresponding homopolymers. The damping curves did not show any peaks in the β-relaxation range, which indicates that the amount of short branching in the copolymers is negligible.

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.

Flory-Huggins interaction parameter of poly(ethylene oxide)/poly(epichlorohydrin) and poly(ethylene oxide)/ poly(epichlorohydrin- co-ethylene oxide) blends

Blends of poly(ethylene) oxide with poly(epichlorohydrin) and poly(epichlorohydrin- co-ethylene oxide) havebeen prepared by the freeze-drying method from benzene solutions of the polymer mixture at different compositions. The miscibility of the mixtures was studied by DSC. A single glass transition temperature is observed for all the blends studied. Measurement of the melting temperature ( T m) depression for the blends allowed determination of the Flory-Huggins interaction parameter (χ 12) of the two polymers in the melt using the Nishi-Wang equation. The Hoffman-Weeks extrapolation was applied to obtain equilibrium T m data. The values of the χ 12 obtained from T m depression data were negative for all blends. This suggests the miscibility of the components of the blends.

Crystallization, melting, and relaxation of modified poly(phenylene sulfide). I. Calorimetric studies

Abstract The crystallization, melting, and glass-rubber relaxation characteristics of a series of random poly(phenylene sulfide) (PPS) copolymers based on sodium hydrosulfide (NaSH) and 1,4- and 1,3-dichlorobenzene monomers have been investigated; sample compositions included the PPS homopolymer, and copolymers incorporating 5%, 8%, and 10% meta-phenylene linkages. The introduction of increasing levels of meta-phenylene units led to a modest decrease in amorphous glass transition temperature (from 86°C [0%] to 74°C [10%]) and a strong decrease in equilibrium melting temperature as determined by Hoffman-Weeks extrapolation(from 331°C[0%] to 273°C [10%]). Wide-angle x-ray scattering (WAXS) studies indicated that the meta units were excluded as defects from the bulk crystal structure, with no variation in unit cell parameters. Measurements of glass transition temperature for the crystallized polymers revealed a significant positive offset in Tg with the presence of crystallinity owing to the constraints impo...

Physical properties of syndiotactic polypropylene

Abstract Crystallization and melting, heat of fusion, and degree of crystallinity of syndiotactic PP were investigated. The double peak melting behavior was established for the partially crystalline polymer. A Hoffman-Weeks extrapolation resulted in equilibrium melting points of 151°C and 155°C for two polymers with relatively short syndiotactic sequences. The enthalpy of fusion was found to be 200 J/g, which corresponds to the value of isotactic pp. A very close correlation between the syndiotactic IR index and the heat of fusion was found. The melting point dependence on the sequence length was evaluated.