Theory Of Melting Point Depression Research Articles

A versatile lead iodide particle synthesis and film surface analysis for optoelectronics

Lead (II) iodide, PbI2, semiconductor was synthesized using versatile methods such as hydrothermal, refluxing, solid-state reaction, and co-precipitation for optoelectronics. All the PbI2 particles exhibited hexagonal-layered 2H structure in which the average crystallite size and optical bandgap (Eg) were 57 ± 10 nm and 2.31 eV, respectively. Then, PbI2films were prepared using dimethyl sulfoxide (DMSO) or dimethylformamide (DMF) on the top of a mesoporous TiO2 layer, yielding a wider Eg of 2.33–2.36. Finally, through water contact angle measurement, the surface and interfacial properties of the thin film were characterized, exhibiting initial solid-vapor surface tension (γsv) of 6.1–6.4 mJ/m2 and solubility parameter (δ) of 4.51–4.62 (cal/cm3)1/2. However, when these PbI2 films were exposed to H2O molecules in air, δ changes from 4.62 to 7.28 (cal/cm3)1/2 for PbI2 (DMSO) film or 4.51 to 12.98 (cal/cm3)1/2 for the PbI2 (DMF) film, respectively. Finally, by employing the theory of melting point depression combined with the Flory-Huggins lattice theory, the interfacial interactions between PbI2 and regioregular poly (3-hexylthiophene-2,5-diyl) were qualitatively characterized. The smaller the χ interaction parameter, the more depressed the melting point.

Phase Diagrams of n-Type Low Bandgap Naphthalenediimide-Bithiophene Copolymer Solutions and Blends.

Phase diagrams of n-type low bandgap poly{(N,N′-bis(2-octyldodecyl)naphthalene -1,4,5,8-bis(dicarboximide)-2,6-diyl)-alt-5,5′,-(2,2′-bithiophene)} (P(NDI2OD-T2)) solutions and blends were constructed. To this end, we employed the Flory–Huggins (FH) lattice theory for qualitatively understanding the phase behavior of P(NDI2OD-T2) solutions as a function of solvent, chlorobenzene, chloroform, and p-xylene. Herein, the polymer–solvent interaction parameter (χ) was obtained from a water contact angle measurement, leading to the solubility parameter. The phase behavior of these P(NDI2OD-T2) solutions showed both liquid–liquid (L–L) and liquid–solid (L–S) phase transitions. However, depending on the solvent, the relative position of the liquid–liquid phase equilibria (LLE) and solid–liquid phase equilibria (SLE) (i.e., two-phase co-existence curves) could be changed drastically, i.e., LLE > SLE, LLE ≈ SLE, and SLE > LLE. Finally, we studied the phase behavior of the polymer–polymer mixture composed of P(NDI2OD-T2) and regioregular poly(3-hexylthiophene-2,5-dyil) (r-reg P3HT), in which the melting transition curve was compared with the theory of melting point depression combined with the FH model. The FH theory describes excellently the melting temperature of the r-reg P3HT/P(NDI2OD-T2) mixture when the entropic contribution to the polymer–polymer interaction parameter (χ = 116.8 K/T − 0.185, dimensionless) was properly accounted for, indicating an increase of entropy by forming a new contact between two different polymer segments. Understanding the phase behavior of the polymer solutions and blends affecting morphologies plays an integral role towards developing polymer optoelectronic devices.

Order–Disorder Phase Equilibria of Regioregular Poly(3-hexylthiophene-2,5-diyl) Solution

The cloud-point curves for solutions of regioregular poly(3-hexylthiophene-2,5-diyl) (P3HT) in o-dichlorobenzene as a function of composition were measured using a thermooptical analysis method. The binary polymer solution shows phase equilibria between a single coiled polymer in solution and polymer in nanocrystalline aggregation, in which the coexistence points at the melting temperature (i.e., solid–liquid equilibria) could be described by the theory of melting point depression combined with the Flory–Huggins model. Through the correlation of theory and experimental data, the heat of fusion per crystalline repeat unit (ΔHu = 47.5 J/g) and the binary interaction parameter (χ = 32.6/T) were estimated. When the solutions were further characterized using UV–vis spectroscopy and X-ray diffraction (XRD), the absorption spectra showed a red-shift (λmax = 464 to 518 nm) with increasing P3HT concentration from 0.01 to 6 wt %, and the XRD data displayed a trace of (100) peaks at 2θ = 5.39° with d-spacing of 1.6 ...

Effect of Hydroxyl-Functionalization on the Structure and Properties of Polypropylene

Hydroxyl-modified polypropylenes (PPOH) with side chains containing OH groups were synthesized by copolymerization of the propylene and undecenyloxytrimethylsilane monomers. Copolymers with hydroxyl concentration up to ∼4 mol % were produced by hydrolysis of the propylene–undecenyloxytrimethylsilane copolymers and their structural, thermal and rheological properties were compared with that of unmodified polypropylene (PP). The presence of H-bonding between the hydroxyl groups led to a densification of the amorphous domains and an increase in the glass-transition temperature with increasing hydroxyl concentration. The incorporation of comonomer in the PP backbone led to a reduction in the melting point, as predicted by Flory’s theory of melting point depression in copolymers. During crystallization, the OH containing polymer segments are excluded from the crystalline domains and their presence disrupt the growth behavior leading to reduced lamellar thickness, leaving the α-monoclinic crystal structure unaf...

Effects of Thermal Denaturation on the Solid-State Structure and Molecular Mobility of Glycinin

The effects of moisture and thermal denaturation on the solid-state structure and molecular mobility of soy glycinin powder were investigated using multiple techniques that probe over a range of length and time scales. In native glycinin, increased moisture resulted in a decrease in both the glass transition temperature and the denaturation temperature. The sensitivity of the glass transition temperature to moisture is shown to follow the Gordon-Taylor equation, while the sensitivity of the denaturation temperature to moisture is modeled using Flory's melting point depression theory. While denaturation resulted in a loss of long-range order, the principal conformational structures as detected by infrared are maintained. The temperature range over which the glass to rubber transition occurred was extended on the high temperature side, leading to an increase in the midpoint glass transition temperature and suggesting that the amorphous regions of the newly disordered protein are less mobile. (13)C NMR results supported this hypothesis.

Electrochemical properties for ionic liquid/polymer electrolyte systems

The ionic liquid (1-ethyl-3-methylimidazolium hexafluorouphophate) ([emim][PF6]) with different molecular weights of poly(ethylene oxide) (PEO) (MW = 4600; 10,000; 14,000; 20,000; 35,000, and 100,000) has been characterized at various temperatures and compositions using phase behaviors and ionic conductivity. A molecular thermodynamic model based on a combination of the previous theory (BH model) by Chang et al., a nonrandomness theory (NR model), and the Pitzer-Debye-Hückel theory modified by Guggenheim (PDH model) considered not only short-range specific interactions between the polymer and a cation of the ionic liquid (IL), but also long-range electrostatic forces between anions and cations within the IL. We have derived a new melting point depression theory based on this BH-NR-PDH model. We also established an ionic conductivity model, based on the Nernst-Einstein equation, in which the diffusion coefficient is derived from the BH-NR-PDH model. The proposed model takes into account that the mobility of cations in the IL and the motions of the polymer host by expressing the effective chemical potential as the sum of the chemical potentials of the polymer and the IL. To describe the segmental motion of the cation and polymer chain, the effective coordinated unit parameter is introduced. The derived coordinated unit parameter for each state is used to determine the ionic conductivities of the given systems. Quantitative results from the proposed model are in good agreement with experimental data. The results indicate that the molecular weight of the polymer and the surrounding temperature play important roles in determining eutectic points and ionic conductivities of the given systems. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 212–219, 2010

Phase behaviors of polymer blend(PEO–PPO) electrolyte/LiCF3SO3 systems in lithium battery

AbstractPolymer blend (poly(ethylene oxide) (PEO)–poly(propylene oxide) (PPO)) systems with two different mole ratios, complexed with LiCF3SO3 salt, have been characterized at various temperatures and compositions using a thermo‐optical analysis (TOA) technique. We also developed a new melting point depression theory based on the modified perturbed hard sphere chain model to interpret phase behavior of polymer blend electrolyte systems. The obtained results show that the eutectic points move toward higher Tm and lower weight fraction of salt with decreasing PEO mole ratio and also indicate that the mole ratio of PEO–PPO for each polymer blend plays an important role in determining the eutectic point of the polymer blend system. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 2314–2319, 2005

Phase behaviors of solid polymer electrolyte/salt systems in lithium secondary battery: the ionic interaction and nonrandomness effect

We establish a new melting point depression theory based on the modified double lattice (MDL) model. The proposed work takes into account the long-range interactions caused by the Coulombic interaction between ions and the local composition concept to describe phase behaviors of the solid polymer electrolyte/salt system. The ionic contribution is described by the Pitzer–Debye–Hückel (PDH) ion interaction model and the nonrandom factor proposed by Panayiotou et al. Systems studied in this work are binary mixtures of PEO and various salts. Results show that the ionic interaction and nonrandomness effect of the salt distribution play a major role in determining eutectic points of the given systems. When compared with experimental data, quantitative descriptions of the proposed model show better agreement for the given systems than those of the original MDL model.

Phase behaviors of hyperbranched solid polymer electrolyte/salt systems: The structure effect

AbstractWe have derived a new molecular thermodynamic model based on the lattice cluster model and melting point depression theory to account for the structural effect on phase behaviors of hyperbranched solid polymer electrolyte/salt systems. The two structural parameters (the generation number and separator length) are introduced to characterize the architecture of the hyperbranched polymer. A thermooptical analysis technique is used to determine the melting points of hyperbranched polymer/ZnI2 systems. Our results show that the eutectic point is presented at a higher weight fraction of the salt as the generation number increases. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2254–2262, 2004

Theoretical consideration on phase behaviors of poly(ethylene oxide-block-propylene oxide)/LiCF 3SO 3 systems in lithium battery

A new thermodynamic model is developed based on the extended perturbed hard sphere chain (PHSC) model and melting point depression theory to describe the phase behaviors of copolymer electrolyte/salt systems. The phase behaviors of poly(ethylene oxide-block-propylene oxide)/LiCF 3SO 3 systems are investigated by thermo-optical analysis (TOA) technique. Quantitative descriptions according to the proposed model are in good agreement with experimental data. The obtained results show that monomer ratio and sequence type of copolymers play a great role in determining eutectic points of the given systems.

Theory of melting point depression for SPE/salt systems; applicability of the extended PHSC model

We derive a new melting point depression theory based on the extended perturbed hard sphere chain (PHSC) model to interpret phase behaviors of solid polymer electrolyte systems with various salts. Quantitative descriptions according to the proposed model are in good agreement with experimental data for the given systems. The obtained results show that the salt weight fraction and the size of salt molecule play a great role in determining eutectic points of the given systems.

The effect of pressure on phase behaviors of solid polymer electrolyte/salt systems in lithium battery

A molecular thermodynamic model based on the theory of melting point depression and the modified double lattice model with the free-volume effect is developed to interpret phase behaviors of solid polymer electrolyte (SPE)/salt systems with various pressures. To account for the free-volume effects, we employ the hole-theory proposed by Kleintjens. Quantitative description according to the proposed model is in good agreement with the experimentally observed transition temperatures for given systems. Our results show that eutectic points move toward higher T m and lower weight fraction region of salt with increasing pressure.

Effect of compression on the solid polymer electrolytes: The modified lattice‐fluid model

AbstractA molecular thermodynamic model based on the theory of melting point depression, the Adam–Gibbs configurational entropy model, and the modified lattice‐fluid model was developed to interpret ionic conductivities of solid polymer electrolytes with various pressures. A new configurational entropy, S was introduced in this model. Quantitative descriptions according to the proposed model agreed with the experimental data for the given systems. Our results showed that a eutectic point moves toward higher melting temperatures, whereas a lower weight fraction of salt and the ionic conductivity significantly decrease with pressure. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 706–713, 2002

Ionic conductivities of solid polymer electrolytes: The effect of pressure

AbstractA molecular thermodynamic model based on the theory of melting point depression, the Adam–Gibbs configurational entropy model, and the lattice fluid model was developed to interpret the ionic conductivities of solid polymer electrolytes with various pressures. Quantitative descriptions according to the proposed model are in good agreement with the experimental data for the given systems. Our results show that an eutectic point moves toward a higher Tm and lower weight fraction of salt, and the ionic conductivity significantly decreases with pressure. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1484–1491, 2001

The effect of compression on the solid polymer elecrolytes: Consideration of specific interaction

A thermodynamic model taking into account of the specific interaction between polymer and salt is proposed. We employed the theory of melting point depression and the generalized lattice-fluid (GLF) model to interpret the liquidus curves in the resulting phase diagram and to describe the change of liquidus curves and an eutectic point at various pressure. The quantitative description according to the proposed model is in good agreement with the experimentally observed transition temperature of a given system. Results show that an eutectic point moves toward higher Tm and lower weight fraction of salt with increasing pressure.

Phase behaviors of solid polymer electrolyte–salt systems: the effect of pressure

A molecular thermodynamic model based on both the theory of melting point depression and the lattice fluid model is developed to interpret the liquidus curves in the resulting phase diagram and predict the change of liquidus curve and an eutectic point with various pressures. Quantitative description according to the proposed model is in good agreement with the experimentally observed transition temperature of a given system and shows that an eutectic point moves toward higher T m and lower weight fraction of salt with increasing pressure.

Membrane formation via phase separation induced by penetration of nonsolvent from vapor phase. I. Phase diagram and mass transfer process

The isothermal phase diagram for poly(vinylidene fluoride)/dimethyl formamide/water system was derived. The binodal and spinodal were calculated based on the Flory–Huggins theory and the calculated binodal was approximately in agreement with the experimental data of the cloud points. The isothermal crystallization line was also obtained according to the theory of melting point depression. Mass transfer of the three components during membrane formation by the precipitation from the vapor phase has been analyzed. During this process, phase separation of the polymer solution is induced by the penetration of water vapor in the solution. The calculated result on the changes of the cast film weights indicated the good agreement with the experimental data. The time-course of the polymer concentration profile in the film was calculated for various cases of different humidity of the vapor phase and different initial polymer concentration. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 159–170, 1999

Studies of macromolecular entanglements. I. Melting behavior of swelling polymers with macromolecular entanglements

AbstractIn this paper the swelling and melting behavior of several polymers, particularly acrylic fibers, is studied by thermomicroscopy and differential scanning calorimetry in detail. It is confirmed that the protrusion peak on the tail part of the DSC thermogram of swelling polymers is closely associated with the macromolecular entanglements. The proposed swelling DSC method is proved to be very effective for studying polymer entanglements. It is also shown that the melting point, whether of paracrystalline region or of entanglement structural unit, can be well fitted to Flory's melting point depression theory.

General crystallization behaviour of poly( l-lactic acid) PLLA: 2. Eutectic crystallization of PLLA

The solidification and melting behaviour of quasi-binary systems formed by poly( l-lactic acid) (PLLA) and respectively the diluents parahydroxybenzoic acid (PHBA) and hexamethylbenzene (HMB) have been investigated. For both quasi-binary systems the effect of diluent concentration on the measured melting temperatures was in reasonable agreement with the theoretical values calculated according to the Flory-Huggins theory of melting point depression. The PLLA-PHBA system formed an eutectic composition for 84% w/w of PLLA in the mixture. Its eutectic melting temperature is 437K. For the PLLA-HMB system the eutectic composition was 65% w/w of PLLA in the mixture and the eutectic melting temperaturre of 432K. The morphology of the PLLA-diluent mixtures was strongly dependent on the diluent concentration. Fracture surfaces of the mixtures of PLLA and PHBA exhibited faceted crystals of various shape, formed by the diluent. They could not be removed from the polymer by sublimation, probably because of the intermolecular hydrogen bonds formed by PHBA itself and/or PHBA and the PLLA matrix. Sublimation of diluent from PLLA-HMB quasi-binary system led to a highly porous material of varying morphology.

Eutectic solidification and oriented growth in mixtures of polyethylene and 1,3,5-tribromobenzene

The melting and crystallization behaviour of mixtures of linear polyethylene and 1,3,5-tribromobenzene has been investigated by differential scanning calorimetry, optical and electron microscopy. The phase diagram reveals the existence of a pseudo-binary eutectic (polymer volume fraction of about 58%; T m=116°C). The experimental observations are compared with the predictions of the Flory-Huggins theory of melting point depression. The polyethylene component of the eutectic assumes a habit in which lamellae are highly oriented with the chains in the [110] contact plane parallel to the tribromobenzene needle axes. This well defined orientation is most probably based on an epitaxial relation between polymer and substrate.