Polymer crystallization dynamics,as reflected by differential scanning calorimetry. Part 2: Numerical simulations

With the aid of a model for the kinetics of polymer crystallization, as put forward in previous publications, the shape of DSC-curves and their position on the temperature scale were simulated for various conditions of heat transfer in the apparatus. It turns out that the outcome is very dependent on the assumptions made with respect to these heat transfer conditions. For the ideal condition — no temperature differences between sample, pan and furnace — an invariable shape is predicted for the DSC-curves. They only shift to lower temperatures with increasing cooling rates. For more realistic conditions, the curves not only shift but become broader and their maxima decrease. They show a more familiar appearance. These calculations are very involved, however, A simple balance equation is shown to yield equivalent results, if a dimensionless characteristic number like the Nusselt number remains considerably smaller than one. This number contains an effective heat transfer coefficient between sample and furnace which, surprisingly, should not be too high. Apparently, the heat capacity of the pan does not play an important role under these conditions. This is investigated in Appendix II. Appendix I describes the procedure of the numerical simulations.     

PHOTOACOUSTIC DETECTION OF TRIPLET STATE AND SINGLET OXYGEN IN HIGHLY ABSORBING SAMPLES

A photoacoustic (PA) effect theory taking into account two heat sources corresponding to the radiationless relaxation processes of two states of different lifetimes and to the heat diffusion across the sample is herewith presented. Results obtained demonstrate that the amplitude and the phase of the PA signal depend on the sample's thermal properties, on its optical absorption coefficient, on the lifetime of the long-lived excited state, and on the ratio of the two heat sources. This ratio can be expressed as a function of the product of the energy of the excited state times the quantum yield of its production. Simulations of PA amplitude and phase variations vs light modulation frequency exhibit new features of the PA signal:phase inversion and fast decrease of the amplitude. Experimental verifications were carried out on solutions and gels. Fitting of the amplitude and phase variations allow us to measure the lifetime and conversion yield of the intermediate state which can be a triplet state or singlet oxygen, O2(1 delta g). The addition of an acceptor, specific to O2(1 delta g), induces changes in the amplitude of the PA signal which can be used to study the production and deactivation of this excited form of oxygen. This work demonstrates the usefulness of PA in the detection of metastable excited states such as the triplet state and singlet oxygen and in their quantitative analysis.     

A Method for Analysis of the Measured Curves of TMDSC Investigation in the Melting Region of Polymers

The measured signal of the temperature-modulated differential scanning calorimetry (TMDSC) is discussed in the case of polymer melting. The common data evaluation procedure of TMDSC-signals is the Fourier analysis. The resulting information is the amplitude and the phase shift of the first harmonic of the periodic heat flow component. It is shown that this procedure is not sufficient for quantitative discussions if deviations from the symmetric curve shape occur in the measured heat flow curves. For polymer melting it is demonstrated that asymmetric curves will be measured if the experimental temperature amplitude is too large. In this paper a data evaluation method is presented, which is based on the Fourier transform of the measured curves. The peaks of the first and second harmonics in the resulting spectra are used for the analysis of the asymmetry of the measured curves. In the case of polymer melting this analysis yields the maximum temperature amplitude which follows a correct linear data evaluation. This maximum temperature amplitude depends on the material. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fingering of exothermic reaction-diffusion fronts in Hele-Shaw cells with conducting walls

We consider the influence of heat losses through the walls of a Hele-Shaw cell on the linear stability and nonlinear dynamics of exothermic chemical fronts whose solutal and thermal contributions to density changes have the same signs. Our analysis is based on the reaction-diffusion-convection equations obtained from the Darcy-Boussinesq approximation. The parameters governing the equations are the Damkohler number, a kinetic parameter d, the Lewis number Le, the thermal-expansion coefficient gammaT, and a heat-transfer coefficient alpha which measures heat losses through the walls. We show that for thermally insulating walls, the temperature profile is a front that follows the concentration profile, while in the presence of heat losses, the temperature profile becomes a pulse that leads to a nonmonotonic density profile which in turn may lead to a destabilization of an otherwise stable front.     

Theorie der Wärmeübergänge bei DSC-Messungen

Zusammenfassung Der Einfluss von Wärmeübergängen auf das Wärmeflussignal von Wärmeleit- und Leistungskompensations-DSC-Messungen wird unter Voraussetzung möglichst praxisnaher Bedingungen exakt berechnet. Dabei werden sowohl die Wärmeübergänge vom Tiegel zur Probenkapsel und von der Probenkapsel zur Probe als auch von der Probenkapsel zur Umgebung mit berücksichtigt. Die erhaltenen Ergebnisse können zur Interpretation und Fehlerbestimmung der experimentell erhaltenen DSC-Kurven benutzt werden. Als wichtigstes Resultat wird erhalten, dass die Güte einer DSC-Messung bei vorausgesetzter Symmetrie der Wärmekapazitäten vor allem von der Grössenordnung der Wärmeübergänge abhängt.Trotz völliger Symmetrie aller Bauteile können Wärmeverluste und Kontaktprobleme, unabhängig von ihrer Symmetrie, erhebliche Messfehler verursachen. Schlussfolgerungen für die praktische Durchführung von DSC-Messungen werden abgeleitet.

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The influence of heat-transfer coefficients on the heat-flux-signal of usual and power compensated DSC methods is exactly calculated on the supposition of practice-relevant conditions, in which not only heat-transfer from sample holder to pan and from pan to sample but also heat-transfer to the environment is taken into consideration. The recieved results can be used to interpret and determine the faults of the experimentally obtained DSC curves.On the understanding of the symmetry of the heat capacities the most important result is, that the quality of the DSC-signal is mainly dependent on the magnitude of the heattransfer coefficients.In spite of full symmetry of all parts heat losses and contact problems can cause considerable errors independent of symmetry of the heat losses and contact resistances. Conclusions for the practical accomplishment of DSC measurements are given.

     

Temperature-modulated differential scanning calorimetry of reversible and irreversible first-order transitions

Temperature-modulated differential scanning calorimetry of first-order transitions has led to many new observations. Some of these involve non-linear processes or deal with transformations of practically instantaneous response. The latter may cause serious lags within the calorimeter due to limited thermal conductivity of the sample and the instrument. In both cases the “reversing heat capacity” or a “complex heat capacity” is not a precise representation of the transition since both are computed from abbreviated Fourier transforms, limited to the evaluation of the first harmonic component. One has in these cases to work in the time-domain with the raw output. But even from these analyses in the time-domain many interesting new insights about the transition and the calorimeter performance can be generated.     

Some remarks on heat capacity measurements by temperature-modulated calorimetry

In temperature-modulated calorimetry, the condition in sample amount, especially thickness, required for high-accuracy heat capacity measurement should be made clear. We propose the condition of maximum thickness of a sample for measuring heat capacity within an accuracy of 1%. The other important factor for high-accuracy heat capacity measurement is thermal contact conductance between a sample and a sample pan and also that between a pan and a base plate of an apparatus. The conditions in these thermal contact conductances required for high-accuracy heat capacity measurement are discussed. Among them, if only thermal contact conductance between a pan and a base plate is significant, there is an ingenious method to measure heat capacity with high accuracy. Furthermore, if the thermal contact conductance between a pan and a base plate is infinite, we offer a simple method to obtain complex heat capacity.     

Dual fluorescence of 4-N,N-dimethylaminopyridine. Role of hydrogen-bonded complex in the ground state

A correlation is shown between the appearance of the dual fluorescence of 4-N,N-dimethylaminopyridine (DMAP) solutions and the formation of hydrogen-bonded of complexes in the ground state. A comparative absorption study between pyridine, N,N-dimethylaniline and DMAP shows that the hydrogen-bonded complex is situated on the amino nitrogen of DMAP. A “pretwisted” conformation of DMAP in the ground state isassumed due to this hydrogen-bonded complex. Simulations by intermolecular interaction calculations and spectroscopic calculations (CNDO/s) confrim the “twisting” influence of water molecules (and/or any other hydrogen bonding) on the amine in the ground state. This “pretwisting” in the ground state by hydrogen bonding is common in many other aromatic amines. Moreover, the deforming role of hydrogen bonding in the ground state seems to be a general phenomenon in flexible aromatic molecules.     

Polymer crystallization dynamics,as reflected by differential scanning calorimetry. Part 1: On the calibration of the apparatus

In this paper a method for the calibration of the heat transfer coefficient between pan and furnace is given. This (second) calibration is necessary in addition to the usual calibration of the temperature scale. Indeed, with increasing cooling rates as required for kinetic measurements, the finite heat flow resistance between pan and furnace becomes evident anyway. We also propose to enlarge this resistance deliberately, in order to separate the time scales of the control system and of the exponential return of the heat flow curve to the base line, as occurring after completion of the phase transition. Only in this way can the heat transfer coefficient be determined with some accuracy. Another advantage of a lowered heat transfer coefficient will be treated in a third paper. It enables an approximate treatment of polymer crystallization kinetics.     

Reaction of exciplex formation in the gas phase. The role of weak attractive interactions in the initial state

The reaction of molecular exciplex formation in the gas phase is treated within the framework of the Landau-Zener approximation, with the assumption that the initial state of the reaction has a potential energy curve including both repulsive and attractive interactions. It is found that the introduction of attractive interactions into the initial state (commonly treated as a repulsive state) leads, in the case of dipole-induced-dipole interaction, to a “reverse” temperature dependence of the exciplex formation rate constant.     

调制BZ-CSTR反应体系小振荡诱导非平衡相变

以流量为扰动参数,对连续搅拌釜式反应器（ＣＳＴＲ）中的Ｂｅｌｏｕｓｏｖ－Ｚｈａｂｏｔｉｎｄｓｋｙ（ＢＺ）反应体系小振荡进行周期或噪声扰动,改变扰动周期或扰动强度,在某些条件下可以诱导非平衡相变。以ＢＺ反应的四变量Ｍｏｎｔａｎａｔｏｒ模型为基础,对相应流率区进行周期或噪声扰动,计算结果与实验基本定性一致。     

The nature of the low energy band of the Fenna-Matthews-Olson complex: vibronic signatures

Based entirely upon actual experimental observations on electron-phonon coupling, we develop a theoretical framework to show that the lowest energy band of the Fenna-Matthews-Olson complex exhibits observable features due to the quantum nature of the vibrational manifolds present in its chromophores. The study of linear spectra provides us with the basis to understand the dynamical features arising from the vibronic structure in nonlinear spectra in a progressive fashion, starting from a microscopic model to finally performing an inhomogeneous average. We show that the discreteness of the vibronic structure can be witnessed by probing the diagonal peaks of the nonlinear spectra by means of a relative phase shift in the waiting time resolved signal. Moreover, we demonstrate that the photon-echo and non-rephasing paths are sensitive to different harmonics in the vibrational manifold when static disorder is taken into account. Supported by analytical and numerical calculations, we show that non-diagonal resonances in the 2D spectra in the waiting time, further capture the discreteness of vibrations through a modulation of the amplitude without any effect in the signal intrinsic frequency. This fact generates a signal that is highly sensitive to correlations in the static disorder of the excitonic energy albeit protected against dephasing due to inhomogeneities of the vibrational ensemble.     

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.     

Experimental Considerations for Temperature Modulated DSC at Low Temperature

Temperature modulated DSC (TMDSC) at low temperatures requires attention to the selection of experimental parameters that are within the capability of the instrumentation as well as special care in calibration of heat capacity measurement when high precision is required. Data are presented to facilitate selection of appropriate modulation periods and amplitudes at low temperature when using a mechanical cooling accessory. The standard error of the mean heat capacity measurement for a sapphire standard increased with decreasing temperature, decreasing period, and increasing pan mass. For ice in hermetically sealed pans, the standard error of the mean heat capacity measurement was larger than for sapphire and did not follow a predictable trend with changes in temperature and period of modulation. This was attributed to changes in sample geometry between successive measurements due to melting and resolidification. A simple one-point temperature calibration by TMDSC may be unsuitable for precise measurement of heat capacity because of the random error caused by sample placement and the systematic error caused by cell asymmetry, temperature dependence of the calibration constant, and different sample thermal conductivities. An alternative calibration procedure using standard DSC and either a linear or second order fit of the calibration constant over the temperature range of interest is proposed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Lattice model of equilibrium polymerization. V. Scattering properties and the width of the critical regime for phase separation

Dynamic clustering associated with self-assembly in many complex fluids can qualitatively alter the shape of phase boundaries and produce large changes in the scale of critical fluctuations that are difficult to comprehend within the existing framework of theories of critical phenomena for nonassociating fluids. In order to elucidate the scattering and critical properties of associating fluids, we consider several models of equilibrium polymerization that describe widely occurring types of associating fluids at equilibrium and that exhibit the well defined cluster geometry of linear polymer chains. Specifically, a Flory-Huggins-type lattice theory is used, in conjunction with the random phase approximation, to compute the correlation length amplitude xi(o) and the Ginzburg number Gi corresponding, respectively, to the scale of composition fluctuations and to a parameter characterizing the temperature range over which Ising critical behavior is exhibited. Our calculations indicate that upon increasing the interparticle association energy, the polymer chains become increasingly long in the vicinity of the critical point, leading naturally to a more asymmetric phase boundary. This increase in the average degree of polymerization implies, in turn, a larger xi(o) and a drastically reduced width of the critical region (as measured by Gi). We thus obtain insight into the common appearance of asymmetric phase boundaries in a wide range of "complex" fluids and into the observation of apparent mean field critical behavior even rather close to the critical point.     

Experimental investigation into the heat capacity measurement using an modulated DSC

Experiments using a commercial modulated DSC (MDSC) for the measurement of specific heat capacity of a sample have been carried out. It is found that because the amplitude of heat flow of MDSC is a complicated non-linear function of various experimental conditions such as the modulation frequency and the heat capacities of a sample and pan, the methodology of heat capacity determination using an MDSC in a single run has not been justified. The experimental results, on the other hand, agree with the theoretical equation of one of the authors. It is therefore concluded that the capabilities of MDSC should be further examined.     

The electronic structure of diphenyltin(IV) dichloride, calculation of the mössbauer isomer shift and the quadrupole splitting of tin and the nuclear

Nonrelativistic and quasirelativistic SCF-MS calculations on the diphenyltin(IV) dichloride monomer and possible “dimer”, give theoretical insight into the intermolecular chlorine interaction. This molecule is not a polymer like other diorganotin(IV) dichlorides. A weak interaction occurs in the valence orbital electronic structure; the extent of the interaction is given by the molecular one-electron properties. The isomer shift and the quadrupole splitting of the Mössbauer active ¹¹⁹Sn, and the nuclear quadrupole resonance (n.q.r.) frequency of ³⁵Cl are properties which are helpful in analysing the extent of intermolecular interaction in the “dimer”. The calculated isomer shift and quadrupole splitting agree with experiment. The n.q.r. frequency of ³⁵Cl does not agree well with experiment, which is not a single crystal measurement, but nevertheless the weakness of the intermolecular chlorine interaction was confirmed. Further confirmation comes from the total density plot of (Ph₂SnCl₂)₂.     

Simultaneous measurement of vapor diffusion and solubility coefficients in polymers by frequency response techniques

An experimental technique for the simultaneous measurement of solubility and diffusion coefficients in polymers by frequency response techniques has been developed. A sample of polymer suspended from an electrobalance is exposed to a permeating gas whose pressure is being varied sinusoidally at ultra-low frequencies. The phase angle and amplitude of the weight changes are measured as a function of the frequency of the pressure wave. It is shown that in the linear range the diffusivity coefficient for polyethylene–ethane calculated from the phase angle lag and the Henry's law solubility and the diffusivity obtained from the amplitude ratios are in excellent internal agreement and also agree with values obtained from transient measurements.     

Photoionization cross sections involving an explicitly correlated initial state: Combination of multiconfigurational linear response and the stieltjes—tchebycheff moment theory

We have performed outer valence photoionization cross section calculations for N₂ and O₂. To do this we have combined several linear response techniques, in particular time-dependent Hartree—Fock (TDHF), multiconfigurational time-dependent Hartree—Fock (MC TDHF), and a modification of MC TDHF (MMC TDHF) with Stieltjes—Tchebycheff moment theory (STMT). To our knowledge, these MC TDHF and MMC TDHF calculations are the first which combine explicitly correlated Green function approaches with STMT. Since, in addition, these calculations are fully coupled, we expect the MC TDHF and in particular the MMC TDHF—STMT results to be highly reliable. For both N₂ and O₂ our MC TDHF—STMT and MMC TDHF—STMT results are in overall agreement with previous static exchange STMT results; however, there are a few significant differences and differences in detail in the partial and total photoionization cross sections. In particular, for example, for N₂ we note that the MMC TDHF—STMT does not give a “hump” resonance in the cross section for the (1π_u⁻¹)A²Π_u ionic state. In O₂ we note that the (3σ_g⁻¹) cross section obtained using MMC TDHF—STMT is substantially lower than the static exchange results.