Temperature Modulated DSC of Irreversible Melting of Nylon 6 Crystals

A new method is presented to analyze the irreversible melting kinetics of polymer crystals with a temperature modulated differential scanning calorimetry (TMDSC). The method is based on an expression of the apparent heat capacity, , with the true heat capacity, mc_p, and the response of the kinetics, . The present paper experimentally examines the irreversible melting of nylon 6 crystals on heating. The real and imaginary parts of the apparent heat capacity showed a strong dependence on frequency and heating rate during the melting process. The dependence and the Cole-Cole plot could be fitted by the frequency response function of Debye's type with a characteristic time depending on heating rate. The characteristic time represents the time required for the melting of small crystallites which form the aggregates of polymer crystals. The heating rate dependence of the characteristic time differentiates the superheating dependence of the melting rate. Taking account of the relatively insensitive nature of crystallization to temperature modulation, it is argued that the ‘reversing’ heat flow extrapolated to ω → 0 is related to the endothermic heat flow of melting and the corresponding ‘non-reversing’ heat flow represents the exothermic heat flow of re-crystallization and re-organization. The extrapolated ‘reversing’ and ‘non-reversing’ heat flow indicates the melting and re-crystallization and/or re-organization of nylon 6 crystals at much lower temperature than the melting peak seen in the total heat flow. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solid-solid phase transformation via internal stress-induced virtual melting, significantly below the melting temperature. Application to HMX energetic crystal

We theoretically predict a new phenomenon, namely, that a solid-solid phase transformation (PT) with a large transformation strain can occur via internal stress-induced virtual melting along the interface at temperatures significantly (more than 100 K) below the melting temperature. We show that the energy of elastic stresses, induced by transformation strain, increases the driving force for melting and reduces the melting temperature. Immediately after melting, stresses relax and the unstable melt solidifies. Fast solidification in a thin layer leads to nanoscale cracking which does not affect the thermodynamics or kinetics of the solid-solid transformation. Thus, virtual melting represents a new mechanism of solid-solid PT, stress relaxation, and loss of coherence at a moving solid-solid interface. It also removes the athermal interface friction and deletes the thermomechanical memory of preceding cycles of the direct-reverse transformation. It is also found that nonhydrostatic compressive internal stresses promote melting in contrast to hydrostatic pressure. Sixteen theoretical predictions are in qualitative and quantitative agreement with experiments conducted on the PTs in the energetic crystal HMX. In particular, (a) the energy of internal stresses is sufficient to reduce the melting temperature from 551 to 430 K for the delta phase during the beta --> delta PT and from 520 to 400 K for the beta phase during the delta --> beta PT; (b) predicted activation energies for direct and reverse PTs coincide with corresponding melting energies of the beta and delta phases and with the experimental values; (c) the temperature dependence of the rate constant is determined by the heat of fusion, for both direct and reverse PTs; results b and c are obtained both for overall kinetics and for interface propagation; (d) considerable nanocracking, homogeneously distributed in the transformed material, accompanies the PT, as predicted by theory; (e) the nanocracking does not change the PT thermodynamics or kinetics appreciably for the first and the second PT beta <--> delta cycles, as predicted by theory; (f) beta <--> delta PTs start at a very small driving force (in contrast to all known solid-solid transformations with large transformation strain), that is, elastic energy and athermal interface friction must be negligible; (g) beta --> alpha and alpha --> beta PTs, which are thermodynamically possible in the temperature range 382.4 < theta < 430 K and below 382.4 K, respectively, do not occur.     

Thermal and kinetic study of the ferroelectric phase transition in deuterated triglycine selenate

The specific heat and the enthalpy variation of a highly deuterated crystal of ferroelectric triglycine selenate have been measured around its first-order phase transition using the technique square modulated differential thermal analysis (SMDTA). The low temperature variation rate has allowed analyzing the kinetics of the phase transition. Due to an internal crack in the sample, the transition is carried out in two steps and an intermediate region where the transition is blocked and both phases coexist without transformation has been found. The latent heat on cooling (L _c=1.32±0.02 J g^–1) is higher than on heating (L _h=1.08±0.02 J g^–1) due to the thermal hysteresis and the great difference between the specific heat in both phases. Nevertheless, the enthalpy balance is fulfilled on heating and on cooling.     

Reversibility of the low‐temperature transitions of polytetrafluoroethylene as revealed by temperature‐modulated differential scanning calorimetry

Temperature‐modulated differential scanning calorimetry reveals distinct differences in the kinetics of the low‐temperature phase transitions of polytetrafluoroethylene. The triclinic to trigonal transition at 292 K is partially reversible as long it is not complete. As soon as the total sample is converted, supercooling is required to nucleate the reversal of the helical untwisting involved in the transition. The trigonal phase can be annealed in the early stages after transformation with a relaxtion time of about 5 minutes. The dependence of the reversing heat capacity on the modulation amplitude, after a metastable equilibrium has been reached, is explained by a non‐linear, time‐independent increase of the heat‐flow rate, perhaps caused by an increased true heat capacity. The order‐disorder‐transition at 303 K from the trigonal to a hexagonal condis phase is completely reversible and time‐independent. It extends to temperatures as low as the transition at 292 K or even lower. Qualitatively, the thermal history and crystallization conditions of polytetrafluoroethylene do not affect the transition kinetics, that is, melt‐crystallized film and as‐polymerized powders show similar transition behaviors, despite largely different crystallinities. © 2001 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 750–756, 2001     

On the kinetics of melting and crystallization of poly(l-lactic acid) by TMDSC

The crystallization and melting process of poly(l-lactic acid), PLLA, is investigated by temperature modulated differential scanning calorimetry, TMDSC. The sample is cooled from the melt to different temperatures and the crystallization process is followed by subjecting the material to a modulated quasi-isothermal stage. From the average component of the heat flow and the application of the Lauritzen–Hoffman theory two crystallization regimes are identified with a transition temperature around 118 °C. Besides, the oscillating heat flow allows calculating the crystal growth rate via the model proposed by Toda et al., what gives, in addition, an independent determination of the transition temperature from modulated experiments. Further, the kinetics of melting is studied by modulated heating scans at different frequencies. A strong frequency dependence is found both in the real and imaginary part of the complex heat capacity in the transition region. The kinetic response of the material to the temperature modulation is analyzed with the model proposed by Toda et al. Finally, step-wise quasi-isothermal TMDSC was used to investigate the reversible surface crystallization and melting both on cooling and heating and a small excess heat capacity is observed.     

The Thermodynamic Driving Force for Kinetics in General and Enzyme Kinetics in Particular

The thermodynamic driving force of a reaction is usually taken as the chemical potential difference between products and reactants. The forward and backward reaction rates are then related to this force. This procedure is of very limited validity, as the resulting expression contains no kinetic factor and gives little information on reaction kinetics. The transformation of the reaction rate as a function of concentration (and temperature) into a function of chemical potential should be more properly performed, as illustrated by a simple example of an enzymatic reaction. The proper thermodynamic driving force is the difference between the exponentials of the totaled chemical potentials of reactants and products.     

Diffusion of condensable vapors in single adsorbent particles measured via concentration-swing frequency response

A concentration-swing frequency response method is extended to examine mass transfer mechanisms and the concentration dependence of mass transfer rates for adsorption of condensable vapors in single adsorbent particles. The adsorption kinetics of water and hexane in BPL activated carbon and the adsorption of water in silica gel are determined at several different concentrations. The mechanism that best describes the adsorption of water in BPL activated carbon is nanopore diffusion. The diffusivity of water in BPL activated carbon has a clear minimum at approximately P/Po = 0.5, and the concentration dependence of the diffusion data are not described well by the Darken relationship. Both nanopore diffusion and the Glueckauf linear driving force models can be used to describe the diffusion of hexane in BPL activated carbon for the pressure range studied, and the dependence of the diffusivity on concentration can be described approximately using the Darken relationship. However, the diffusion of water in silica gel cannot be described by the nanopore diffusion model and is best characterized by the Glueckauf linear driving force model. The results illustrate the ability of concentration-swing frequency response to accurately determine adsorption rate mechanisms and quantify the complex adsorption kinetics of condensable vapors using small quantities of adsorbent.     

Hydrate film growth on the surface of a gas bubble suspended in water

The lateral film growth rate of CH4, C2H4, CO2, CH4 + C2H4, and CH4 + C3H8 hydrates in pure water were measured at four fixed temperatures of 273.4, 275.4, 277.4, and 279.4 K by means of suspending a single gas bubble in water. The results showed that the lateral growth rates of mixed-gas CH4 + C2H4 hydrate films were slower than that of pure gas (CH4 or C2H4) for the same driving force and that of mixed-gas CH4 + C3H8 hydrate film growth was the slowest. The dependence of the thickness of hydrate film on the driving force was investigated, and it was demonstrated that the thickness of hydrate film was inversely proportional to the driving force. It was found that the convective heat transfer control model reported in the literature could be used to formulate the lateral film growth rate v(f) with the driving force DeltaT perfectly for all systems after introduction of the assumption that the thickness of hydrate films is inversely proportional to the driving force DeltaT; i.e., v(f) = psiDeltaT(5/2) is correct and independent of the composition of gas and the type of hydrate. The thicknesses of different gas hydrate films were estimated, and it is demonstrated that the thicknesses of mixed-gas hydrate films were thicker than those of pure gases, which was qualitatively consistent with the experimental result.     

Temperature modulated differential scanning calorimetry (TMDSC) in the region of phase transitions. Part 1: theoretical considerations

For temperature modulated differential scanning calorimetry (TMDSC) a simple model, the low pass filter, is presented which allows to see and calculate the influence of heat transfer into the sample on magnitude and phase shift of the modulated part of the measured heat flow rate and the heat capacity determined from it. A formula is given which enables to correct the measured magnitude of the periodic heat flow rate function and the calculated heat capacity in dependence on the thermal resistance and heat capacity of the sample. The correction becomes very important in regions where the heat capacity changes considerably as in the melting region. The approach is successfully tested with model substances with well-known excess heat capacity in the transition region.     

Matching Cure Characteristics of Automotive Rubber Compound and Polyurethane Coating

The present investigation focuses on matching cure characteristics of EPDM rubber compound and polyurethane (PU) coating using temperature modulated and pressure differential scanning calorimetry (TMDSC, PDSC). TMDSC provides a detailed and better understanding of the curing process of model rubber system as well as complex automotive rubber compounds. The low level of unsaturation present in EPDM, results in the small heat of vulcanization (2–5 J g^–1), which is difficult to accurately measure using conventional differential scanning calorimetry (DSC). Thus, curing of highly filled EPDM compound was investigated using TMDSC. The kinetics of PU curing was monitored using pressure DSC (PDSC), and heat of curing was determined as 4.2 J g^–1 at 10°C min^–1 heating rate. It is found that complex automotive compounds and the PU coating are curing simultaneously. This revised version was published online in July 2006 with corrections to the Cover Date.     

Study of the crystallization and melting region of PET and PEN and their blends by TMDSC

The cold crystallization and melting of poly(ethylene therephthalate) (PET), poly(ethylene 2,6-naphthalene dicarboxylate) (PEN) and their blends were studied using temperature modulated differential scanning calorimetry (TMDSC) at underlying heating rates of between 1 and 3 K min^-1 and periods ranging from 30 to 90 s. The amplitude of modulation was selected in order to give an instantaneous heating rate β≥0. Heat flow is analyzed by the total heat flow signal o, which is equivalent to the conventional DSC signal, and the reversing heat flow o_REV, which only detects the glass transition and the melting processes. The dependence of the melting region in the reversing heat flow on the frequency of modulation is analyzed. The use of the so-called non-reversing heat flow o_NREV (=o-o_REV)) and the effect of frequency and amplitude on the complex heat capacity are also studied. The results show the complexity of these magnitudes. This revised version was published online in July 2006 with corrections to the Cover Date.     

Heat Transfer in a Disc-Type DSC Apparatus IV. Applicability of the coupled cells model to periodic temperature modulation

The application of non-linear heating programs to a heat-flux DSC apparatus has attracted much attention. On the basis of thermodynamics, the change in enthalpy of a sample during a temperature change ΔT is due, on the one hand to the true heat capacity of the sample ΔT C_pξ and on the other, to the enthalpy of some transformation occurring in the sample Δ_rH Δξ. These contributions can be separated on the basis of the kinetics of the transformation. The coupled cells model of a disc type, heat flux DSC apparatus has been tested, using true heat capacities and a sine modulation of the temperature of the furnace around a constant temperature. In the range from 2 to 60 mHz, the amplitude and phase shift of the calorimetric signal were measured at several frequencies. Theoretical equations, based on the model, and using the thermal Ohm's law explains the results with a reasonable accuracy. A non-linear DSC experiment affords two ways of determination of the heat capacity of a sample making possible a distinction between the enthalpic effect and heat capacity. This revised version was published online in July 2006 with corrections to the Cover Date.     

Measurement of the free-energy dependence of interfacial charge-transfer rate constants using ZnO/H2O semiconductor/liquid contacts

The dependence of electron-transfer rate constants on the driving force for interfacial charge transfer has been investigated using n-type ZnO electrodes in aqueous solutions. Differential capacitance versus potential and current density versus potential measurements were used to determine the energetics and kinetics, respectively, of the interfacial electron-transfer processes. A series of nonadsorbing, one-electron, outer-sphere redox couples with formal reduction potentials that spanned approximately 900 mV allowed evaluation of both the normal and Marcus inverted regions of interfacial electron-transfer processes. All rate processes were observed to be kinetically first-order in the concentration of surface electrons and first-order in the concentration of dissolved redox acceptors. The band-edge positions of the ZnO were essentially independent of the Nernstian potential of the solution over the range 0.106-1.001 V vs SCE. The rate constant at optimal exoergicity was observed to be approximately 10(-)(16) cm(4) s(-)(1). The rate constant versus driving force dependence at n-type ZnO electrodes exhibited both normal and inverted regions, and the data were well-fit by a parabola generated using classical Marcus theory with a reorganization energy of 0.67 eV. NMR line broadening measurements of the self-exchange rate constants indicated that the redox couples had reorganization energies of 0.64-0.69 eV. The agreement between the reorganization energy of the ions in solution and the reorganization energy for the interfacial electron-transfer processes indicated that the reorganization energy was dominated by the redox species in the electrolyte, as expected from an application of Marcus theory to semiconductor electrodes.     

Investigation of Electrochemical Properties of Metalloporphyrin Species at the Liquid/Liquid Interface by Switching Substitutes on the Porphyrin Ring

In order to investigate the electrochemical properties of porphyrin complexes species in biological systems, metalloporphyrin with different substitutes was applied to observe the process of heterogeneous electron transfer (ET) at the interface between two immiscible electrolyte solutions (ITIES) by scanning electrochemical microscopy (SECM). Experimental results demonstrated that the process of electron transfer was affected dramatically by the presence of different substitutes. Our results also show that the rate constant follows Bulter? Volmer kinetics where the rate increases with increasing force at the low driving force, and Marcus inverted region kinetics at the high driving force where the rate decreases.     

Comparison of the Kinetics of Electron Transfer in the Diffusion Limit for the Singlet and Triplet Quenching of Eosin Y by Quinones

Electron transfer (ET) rate constants were determined by means of lifetime measurements for the fluorescence quenching and by laser flash photolysis for the triplet quenching of the dye eosin Y by benzoquinones in acetonitrile. The results represent a new aspect of the dependence of the rate constants with the driving force in the diffusion limit region. That is, the rate constants for singlet quenching in the highly negative region of ΔG_et do not decrease as predicted by Marcus theory, but rather show a small positive dependence on the driving force. However, it is found that, in the same free energy range, the triplet rate constants are lower than those for the singlet process. They also increase with the exergonicity of the reaction, but the dependence with ΔG_et is less marked than that found for the singlet reaction. Even at a Gibbs energy change of ?1.0 eV the triplet quenching rate constants do not reach the theoretical diffusion limit. The results are analyzed using the current theories for diffusion‐mediated ET reactions.     

Periodic force induced stabilization or destabilization of the denatured state of a protein

We have studied the effects of an external sinusoidal force in protein folding kinetics. The externally applied force field acts on the each amino acid residues of polypeptide chains. Our simulation results show that mean protein folding time first increases with driving frequency and then decreases passing through a maximum. With further increase of the driving frequency the mean folding time starts increasing as the noise-induced hoping event (from the denatured state to the native state) begins to experience many oscillations over the mean barrier crossing time period. Thus unlike one-dimensional barrier crossing problems, the external oscillating force field induces both stabilization or destabilization of the denatured state of a protein. We have also studied the parametric dependence of the folding dynamics on temperature, viscosity, non-Markovian character of bath in presence of the external field.     

TOPEM,a new temperature modulated DSC technique

TOPEM is a new temperature modulated DSC technique, introduced by Mettler-Toledo in late 2005, in which stochastic temperature modulations are superimposed on the underlying rate of a conventional DSC scan. These modulations consist of temperature pulses, of fixed magnitude and alternating sign, with random durations within limits specified by the user. The resulting heat flow signal is analysed by a parameter estimation method which yields a so-called ‘quasi-static’ specific heat capacity and a ‘dynamic’ specific heat capacity over a range of frequencies. In a single scan it is thus possible to distinguish frequency-dependent phenomena from frequency-independent phenomena. Its application to the glass transition is examined here.     

Extensional flow-induced crystallization of a polyethylene melt

Measurements of flow-induced orientation and crystallization have been made on a high-density polyethylene melt (HDPE) undergoing a planar extensional flow in a four-roll mill. The HDPE was suspended as a cylindrical droplet at the flow stagnation point in a linear low density polyethylene (LLDPE) carrier phase. Deformation and crystallization of the HDPE droplet phase were monitored using video imaging in conjunction with measurement of the birefringence and dichroism to quantify the in-situ transformation kinetics. Planar deformation rates along the symmetry axis of the molten HDPE phase were on the order of 0.03 s^?1. Measurements of the initial transformation rate following flow cessation at 131.5°C and 133.2°C show a dependence on initial amorphous phase orientation and the total Hencky strain achieved during flow. The flow-induced crystallization rate is enhanced over the quiescent transformation rate by orders of magnitude, however, the dependence on temperature is less dramatic than expected for a nucleation-controlled growth mechanism. Analysis demonstrates that the melting point elevation model cannot account either qualitatively or quantitatively for the phenomena observed, suggesting that alternative explanations for the strong orientation dependence of the transformation rate are needed.     

Quasi-isothermal measurement of frequency dependent heat capacity of semicrystalline polyethylene at the melting temperature using light heating modulated temperature DSC

Frequency dependence of the heat capacity of semicrystalline polyethylene was measured using light heating modulated temperature DSC (LMDSC). The quasi-isothermal measurement was carried out in the melting temperature range of the crystal. Two decades of the frequency, from 0.01 to 1 Hz, was covered by the LMDSC instrument constructed in the author's laboratory. It was found that in the melting temperature range polyethylene exhibited Debye relaxation with the relaxation time of 14 s and had excess heat capacity independent of the kinetics. The excess heat capacity and the relaxation strength could be attributed to the disordered crystals generated during rapid cooling from the molten state and/or its surrounding amorphous region instead of the stable crystals reorganized during the quasi-isothermal measurement.