Einige polymerspezifische Anwendungen der Schwingungsspektroskopie

Zusammenfassung Anhand dreier Beispiele wird erläutert, wie man durch eine Analyse der Frequenzen, Intensitäten und Linienformen konformationsempfindlicher Banden des Schwingungsspektrums Einblick in die Struktur polymerer Festkörper erlangen und die elastischen Eigenschaften der Einzellamellen studieren kann. Im ersten Beispiel wird die Komponentenstruktur des Ramanspektrums von Polyäthylen behandelt. Die Analyse ergibt, daß neben orthorhombisch-kristallinen und schmelzartig-amorphen Bereichen auch übergangsbereiche existieren müssen, in denen die Ketten zwar gestreckt, jedoch lateral ungeordnet gepackt sind. Die Anteile der drei koexistierenden Phasen lassen sich bestimmen. Die beiden anderen Beispiele befassen sich mit der Auswertung der im Niederfrequenzbereich bei Polyäthylen undn-Alkanen auftretenden longitudinalakustischen Schwingungen. Zunächst wird gezeigt, wie man aus Messungen ann-Al-kanen sowohl die elastische KonstanteE _c im Lamelleninnern als auch die zwischenlamellaren Kopplungskräfte ermitteln kann. Des weiteren wird erläutert, welche Schlußfolgerungen sich aus Messungen an einer lösungskristallisierten Polyäthylenprobe bezüglich der Struktur der fehlgeordneten Deckschichten ergeben. Die Messungen sprechen für eine ausgeprägte Anisotropie bei Fortsetzung der Kettenrichtung im Kristallinen in die Deckschicht hinein.

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Summary Analysis of the frequencies, intensities and line shapes of bands which are sensitive to the chain conformation provides insight into the structure of polymeric solids and permits a study of the elastic properties of the lamellae. In a first example we deal with the multicomponent structure of the Raman spectrum of polyethylene. The general appearance of the spectra is indicative for the existence of a transition region in addition to the orthorhombic crystalline phase and a melt-like amorphous phase. In this transition region chains are stretched but have lost their lateral order. The mass fractions of the three coexisting phases can be determined. Two further examples discuss properties of the longitudinal acoustical modes which appear in the low frequency Raman spectrum of polyethylene and n-alkanes. Evaluation of the n-alkane data permits a determination of the crystalline elastic modulusE _e in chain direction and of the interlamellar forces. The frequencies measured for a solution crystallized sample PE speak in favour of a highly anisotropic state of order in the disordered surface layers.

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Mit 6 Abbildungen und 1 Tabelle

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Auf der Herbsttagung der DPG in Berlin 1978 gegebener Fachbericht.     

Low-frequency Raman spectra of odd α,ω-disubstituted n-alkanes

Low-Frequency Raman spectra of odd α,ω-dibromo- and α,ω-dihydroxy-n-alkanes were recorded. The longitudinal acoustic mode (LAM-1) frequencies were assigned by references to the published results for n-alkanes and even α,ω-disubstituted n-alkanes and also by taking account of the effects of end intermolecular forces and end-group masses by use of the chain model of Minoni and Zerbi.     

Volumes of mixing 2,4-dimethylpyridine withn-alkanes

In continuation of our work on excess thermodynamic properties of non-electrolyte solutions containing pyridine bases withn-alkanes, we have determined excess molar volumesV ^E for 2,4-dimethylpyridine + C₆ to C₁₀ n-alkanes at 25°C. For the investigated systems noV ^E values were available in the literature for comparison with our data. The experimentalV ^E was used to test the Prigogine-Flory-Patterson theory (PFP), Extended Real Associated Solutions model (ERAS) and the Treszczanowicz-Benson method (TB).     

Application of urea adduction technique to polluted urban aerosols for the determination of hydrogen isotopic composition of n-alkanes

We examined an applicability of an improved urea adduction technique for the determination of hydrogen isotopic composition (δD) of homologous series of n-alkanes present in polluted urban aerosols using GC/TC/IRMS. Unresolved complex mixture (UCM) of hydrocarbons that interferes with accurate isotope measurements of n-alkanes was removed from n-alkane fraction by a urea adduction method. Recoveries of C₂₀ to C₃₀ n-alkanes during the urea adduction procedure were greater than 90% when the concentrations of total n-alkanes exceed 6.1?µg?mL^?1. Our compound-specific D/H ratios confirm the absence of significant hydrogen isotope fractionation in n-alkanes during urea adduction and recovery of the purified n-alkane fraction. We applied this technique to the urban aerosols that contain a large quantity of UCM to measure δD of C₂₀ to C₃₅ n-alkanes in urban aerosols from Tokyo and Sapporo with an accuracy less than 10‰. We found that the δD values widely ranged from ?38 to ?179‰. Based on the δD values of individual n-alkanes in aerosol samples, we can obtain further information on the sources of aerosol n-alkanes and their source regions, and the atmospheric processes such as long-range transport and atmospheric mixing of air masses of different origin.     

Chain direction elastic modulus of PE crystal and interlamellar force constant of n-alkane crystals from RAMAN measurements

Spectroscopic data can deliver force constants only if the exact chain conformation is known. For the longitudinal acoustic modes (LAM), however, simple linear chain models can be used to yield the effective longitudinal chain modulus from spectroscopic data of oligomer crystals. The model of p-coupled linear chain molecules with N masses and only nearest neighbor interactions was used to investigate the longitudinal acoustic modes with s nodes. The frequencies plotted versus s/N fall onto different branches for different s. The intermolecular coupling and the heavier endmasses shift the LAM branches to higher and lower frequencies, respectively. There exists a value x₀ depending on the masses and force constants, where the branches cut the dispersion curve of the infinite molecule. For s/N ≥ x₀ the effect of endmasses dominates. Low-frequency RAMAN spectra of n-alkanes (N = 20, …, 40 C atoms) were recorded and analyzed. The LAM1 branch runs clearly above a smooth fit through all other LAM data and the origin. This fit approximates to first order the dispersion curve of the infinite PE molecule in an ideal crystal. Its curvature exceeds that of the dispersion curve of the simple linear chain, but is somewhat smaller than that of the dispersion curve of the planar zig-zag chain with rigid bonds. The slope at the origin yields the limiting elastic modulus E_c = 315 GPa in chain direction of crystalline polyethylene. From our measurements on n-alkanes we obtained the frequency shift of LAM1 due to the interlayer coupling and the heavier endmasses. Calculation of the intermolecular coupling constant of the model of a long row of linear chain molecules with the same frequency shift yield the mean value f_l = 2.5 N/m. This value decreases with increasing chain length. The relevance and applicability of the model is discussed. © 1997 John Wiley & Sons, Inc.     

Low-frequency raman-active modes in methoxy-ended and hydroxy-ended oligo(oxyethylene)s

Low-frequency Raman spectra were recorded for α-methyl, ω-methoxy-oligo(oxyethylene)s, C₁E_mC₁ with m in the range 4–25 (i.e., 15–78 atoms). Longitudinal acoustical mode (LAM-1) frequencies were identified and compared with those determined previously for α-hydro, ω-hydroxy-oligo (oxyethylene)s. Nonlinear relationships between LAM-1 frequency and reciprocal chain length were explained as an effect of intermolecular end forces.     

Raman scattering from the longitudinal acoustic mode of oligo-oxyethylene

Low-frequency Raman spectra are reported for monodisperse oligo-oxyethylenes with hydroxy and alkoxy end groups. Assignments are made to the longitudinal acoustic modes. The results are modeled by a rod with a longitudinal modulus E ≥ 2.2 × 10¹⁰ N m^?2 and perturbing forces as large as (alkoxy-ended oligomers) or larger than (hydroxy-ended oligomers) those suggested for the n-alkanes.     

Critical surface tension of poly(vinyl butyral) and poly(vinyl benzal) multilayers and its relation to their surface orientation. I. Effect of surface pressures during deposition

Critical surface tensions γ_c of poly(vinyl butyral) and poly(vinyl benzal) multilayers built up by the Langmuir-Blodgett method were measured with polyhydric alcohols and n-alkanes. The γ_c values of both polymer multilayers increased with increasing pressures of the piston oils used to control pressures of polymers on the water surface during deposition. The γ_c value of poly(vinyl butyral) multilayers built up to lower pressure of the piston oil was approximately consistent with a crystalline hydrocarbon surface, while the γ_c value of the multilayer built up to higher pressure of the piston oil was approximately consistent with a—CH₃ rather than a ? CH₂ ? CH₂? surface. All results for γ_c values of poly(vinyl benzal) multilayers were very close to the γ_c value of benzene ringrich surface. The γ_c value of the multilayer built up to lower pressure of the piston oil almost coincided with the γ_c value for amorphous polystyrene, while the γ_c value for the multilayer built up to higher pressure of the piston oil was in fair agreement with γ_c for an aromatic ring edge in the crystalline state. Values of γ_s^d, the dispersion force contribution to the surface free energy of multilayers calculated by Fowkes' relation, were in fair agreement with the corresponding observed γ_c values, respectively. It is concluded from these measurements that orientations and surface structures in both polymer multilayers are affected by pressure change of piston oils. The properties on monolayers of two polymers at a air-water interface and on barium stearate multilayers are also presented.     

Adiabatic integration formula for the correlation energy functional of the Hartree–Fock density

An adiabatic integration formula for the quantum chemistry correlation energy functional of the Hartree–Fock density, E _c ^QC[n], is presented. The functional E _c ^QC[n] is meant to be added to the completed Hartree–Fock energy to produce the exact ground-state energy of the system under consideration. The initial slope of the integrand in this connection formula is identified as a second-order energy and an explicit expression for the initial slope of the integrand is presented. Our expression should be useful for arriving at new improved approximations to E _c ^QC[n]. Previous numerical results by Huang and Umrigar (1997) Phys Rev A 56:290, for two-electron densities are proved, and a generalization to more than two electrons is presented. Results obtained by means of the present density functional theory correlation energy functionals, when used to approximate the initial slope in our adiabatic integration formula for E _c ^QC[n], are compared against exact numbers. Received: 10 September 1998 / Accepted: 3 February 1999 / Published online: 21 June 1999     

Adsorption and microcalorimetric investigations ofn-butylamine intercalation in α- and γ-zirconium phosphates

The intercalation process ofn-butylamine was investigated. The adsorption ofn-butylamine in interlamellar space had stepwise character in case of both crystalline forms of zirconium phosphate. The intercalatedn-butylamine existed at low concentration as bilayered complex. The reaction heat was determined by a microcalorimetric method. It was found that about 90% of it refers to the neutralization ofn-butylamine and only about 10% is related with surface adsorption (ion exchange). The steps of adsorption are 6.0 J/g and 1.0 J/g reaction heat values, respectively. The enthalpy balance of total process in dilute solution system (c ₀=3.0 vol%) is 14.67 kJ/mol. The calculated value for ion adsorption (exchange) was 1.37 kJ/mol.     

A theoretical study of the photoelectron spectra of dichloroketene with accurate computation of ionization energies via complete basis set limit extrapolation

We calculated the equilibrium geometries and harmonic vibrational frequencies of the ground state and five cationic states of dichloroketene using (TD-)B3LYP, PBE0, and M06/M06-2X approaches. The photoelectron spectra of dichloroketene were simulated by computing Franck-Condon factors. The ionization energies were computed using the CCSD(T) approach with extrapolation to the complete basis set (CBS) limit. We propose two new CBS energy formulas (E = E_CBS + Aexp(-x) + B/(x−1) ⁿ, n = 2 or 3) and compare the performance of different CBS approaches. A new ionic state of dichloroketene belonging to the C_s point group is reported. This state is identified as the first excited state of Cl₂CCO⁺ having a double-well potential-energy curve along the CCO bending mode with a barrier height of 1.335 eV. The simulated photoelectron spectra are in agreement with the experiment. The vertical ionization energies calculated via spectral simulation are more accurate compared with those obtained at the ground-state structure. Among the CBS formulas used, the proposed ansatz with n = 2 performs best, with a mean absolute error of 0.021 and 0.012 eV for the adiabatic and vertical ionization energies, respectively.     

Study of formation of nano-quasicrystals and crystallization kinetics of Zr-Al-Ni-Cu metallic glass

The formation of nano-quasicrystals on isothermal annealing of melt-spun ribbons of Zr_69.5Al_7.5Ni₁₁Cu₁₂ metallic glass has been investigated using transmission electron microscopy (TEM). The crystallization study of this metallic glass has been carried out using differential scanning calorimetry (DSC) in non-isothermal (linear heating) mode. It exhibits two-stage crystallization where the first stage corresponds to the precipitation of icosohedral nano-quasicrystalline phase. This has been confirmed with the help of TEM investigations. The crystallization parameters like the activation energy (E _c) and frequency factor (k ₀) have been derived using the Kissinger peak shift analysis. The activation energies for the first and second crystallization peak are found to be 278 and 295 kJ mol^–1, respectively. The frequency factors obtained for the two peaks are respectively 7.16·10¹⁹ and 1.42·10²⁰ s^–1. E _c, k ₀ and the Avrami exponent (n) have also been derived by fitting the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation for the transformed volume fraction (x) to the crystallization data. JMAK results of E _c for the first and second crystallization peak turn out to be 270 and 290 kJ mol^–1 respectively. However, k ₀ and n are found to be heating rate dependent as reported in similar studies. The values of n for the first crystallization stage ranges between 1.66 and 2.57 indicating diffusion-controlled transformation in agreement with earlier reports.     

Hydrogen bonding effects on the skeletal optical and the longitudinal acoustical modes in long chain molecules and polymers

Raman spectra of stearyl alcohol (n-C₁₈H₃₇OH) indicate that vibrational bands in both the skeletal optical (1000-1200 cm^?1) and longitudinal acoustical (0–500 cm^?1) regions are considerably perturbed by intermolecular hydrogen bonding. The zone interior skeletal stretching mode reflecting phonon dispersion in the v₄ branch of the infinite polyethylene chain is found at 1105 cm^?1, approximately 20 cm^?1 higher than in the corresponding n-alkane. Similarly the single nodal longitudinal acoustical mode (LAM-1) is found shifted by 12 cm^?1 to higher frequency when the expected “mass effect” produced by the ? OH group is considered. This shift is further increased to 16 cm^?1 at ?100°C indicating a further perturbation on this accordion mode due to the increased strength of the hydrogen bond at the low temperatures. The positions of the higher multinodal vibrations, LAM-3 and LAM-5, are also perturbed by the hydrogen bond but by differing amounts. The observation of a low-frequency Raman-active LAM in polytetrahydrofuran [(? CH₂CH₂CH₂CH₂O? )_n] is discussed in conjunction with the expected effects of hydrogen bonding at the lamellar surface.     

Non-isothermal crystallization behaviors of poly(4-methyl-pentene-1)

Non-isothermal crystallization of isotactic poly(4-methyl-pentene-1) (P4MP1) is studied by differential scanning calorimeter (DSC), and kinetic parameters such as the Avrami exponent and the kinetic crystallization rate (Z _c) are determined. From the cooling and melting curves of P4MP1 at different cooling rates, the crystalline enthalpy increases with the increasing cooling rate, but the degree of crystalline by DSC measurement shows not much variation. Degree of crystalline of P4MP1 calculated by wide angle X-ray diffraction pattern shows the same tendency with crystalline enthalpy, indicating that re-crystallization occurs when samples heated above the second glass transition temperature of P4MP1. By Jeziorny analysis, n ₁ value suggests that mainly spherulites’ growth at 2.5 K min⁻¹ transforms into a mixture mode of three-dimensional and two-dimensional space extensions with further increasing cooling rate. In the secondary crystallization process, n ₂ values indicate that the secondary crystallization is mainly the two-dimensional extension of the lamellar crystals formed during the primary crystallization process. The rates of the crystallization, Z _c and t _1/2 both increase obviously with the increase of cooling rate, especially at the primary crystallization stage. By Mo’s method, higher cooling rate should be required in order to obtain a higher degree of crystallinity at unit crystallization time.     

The decomposition kinetics of disilane and the heat of formation of silylene

The static system decomposition kinetics of disilane (\documentclass{article}\pagestyle{empty}\begin{document}${\rm Si}_{\rm 2} {\rm H}_{\rm 6} \mathop {\longrightarrow}\limits^1 {\rm SiH}_{\rm 2} + {\rm SiH}_{\rm 4}$\end{document}, 538–587 K and 10–500 Torr), are reported. Reaction rate constants are weakly pressure dependent, and best fits of the data are realized with RRKM fall-off calculations using logA_1,∞ = 15.75 and E_1,∞ = 52,200 cal. These parameters yield AH_f⁰(SiH₂)₂₉₈ = (63.5 ? E_{b, c}) kcal mol,^?1 where E_{b, c} is the activation energy for the back reaction at 550 K, M = 1 std state. Five other silylene heat-of-formation values (ranging from 63.9 – E_{b, c} to 66.0 - E_{b, c} kcal mol^?1) are deduced from the reported decomposition kinetics of trisilane and methyldisilane, and from the reported absolute and relative rate constants for silylene insertions into H₂ and SiH₄. Assuming E_{b, c} = 0, an average value of ΔH_f⁰(SiH₂) = 64.3 ± 0.3 kcal mol^?1 is obtained. Also, a recalculation of the activation energy for silylene insertion into H₂, based in part on the new disilane decomposition Arrhenius parameters, gives (0.6 + E_{b, c}) kcal mol^?1, in good agreement with theoretical calculations.     

Diffusion Monte Carlo study of correlation in the hydrogen molecule

The diffusion Monte Carlo (DMC) method shows that correlation in H₂ produces a set of three spatial changes: (i) an enhancement in the electron density distribution n( r ) in the left and right anti‐binding regions that include separately the immediate vicinity of each of the two nuclei, (ii) a reduction in n( r ) in the binding region intervening between the two nuclei as a counterbalance, and (iii) a concomitant increase in the equilibrium internuclear separation. It is stressed that the correlation energy E^c (= T^c + V^c) for diatomic molecules be defined by the difference in the total energy between the exact and the Hartree–Fock (HF) variational calculations that are performed at individually optimized internuclear separations. It is this definition that makes it possible to involve a significant contribution from a correlation‐induced change in the equilibrium internuclear separation as part of the correlation energy and to relate (i) and (ii) to (iii) in consistency with the electrostatic theorem. The present calculations fulfill the virial theorem to an accuracy of ?V/T = 2.00 for DMC and ?V^HF/T^HF = 2.000 for HF. The present correlation energy E^c = ?0.0408 hartree is not only in good agreement with the most accurate value previously reported, but also can be analyzed into all its components in accordance with the correlational virial theorem 2T^c + V^c = 0. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Flow of polymer chains and segregation in a flow field with a hybrid simulation

Effects of a flow field (E) on segregation and flow of polymer chains are studied in two dimensions using a hybrid (discrete‐to‐continuum) simulation. The flow rate (j) of polymer chains is found to increase monotonically with E, a linear response in the low field regime followed by a slow approach to saturation in the high field regime. The effective chain permeability (ϕ_c = j/E) varies nonmonotonically on increasing the field E, with a maximum (ϕ_cm) at a characteristic value of the field (in the range 0.2 < E < 2); ϕ_cm depends on the chain length. Chain aggregates exhibit an anisotropic mass distribution due to the field with a molecular bridging at high fields. The longitudinal component of the radius of gyration (R_gx) exhibits a crossover from a random walk (RW) (R_gx ˜ L_c^1/2) at E = 0 to an elongated conformation (R_gx ˜L_c) at E ⪈ 0.2; the transverse component changes from R_gy ˜ L_c^1/2 to R_gy ˜ L_c^1/3. The width of the radial distribution function (ρ(r)) of the monomers increases while its peak varies nonmonotonically with E and is consistent with the observation of anisotropic mass distribution.     

An equation for the calculation of retention indices in temperature-programmed gas chromatography with allowance for the nonlinear variation of the retention parameters ofn-alkanes

In view of the nonlinear variation of the temperature increments ofn-alkanes found previously, the accuracy of the calculations of the retention indices (I _pr) of substances in temperature-programmed capillary gas chromatography carried out in terms of six known equations was verified. A new four-parameter equation was proposed, and a general method for the calculation of its coefficients, suitable for all stationary phases, based on the adjusted retention times ofn-alkanes was suggested. The coefficients of the equation for 12 temperature variation programs were determined. Using the homologous series of methyl esters of fatty acids as an example, it was shown that the proposed equation ensures the minimum error of determination ofI _pr under various conditions. The equation also makes it possible to carry out interpolation and extrapolation calculations. The coefficients of the equation are found using the least-squares method based on data for any 4–5 referencen-alkanes. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 323–327, February, 1997.     

Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E ₁(t)=E ₁+exp(–a _n t+b _n ). In the limit of very large t, this becomes E ₁(t)=E ₁+exp(–a ₁ t+b ₁). A simple analysis shows that the parameters are a ₁=E ₂–E ₁ and b ₁=ln[(E ₂–E ₁)|c ₂|²/|c ₁|²]. Functions are introduced which allow determination of a ₁, b ₁ and lower bounds to E ₁.     

Evolution of crystallinity in photodegraded polyethylene films studied by ft-raman spectroscopy

FT-Raman spectroscopic studies of photodegraded polyethylene films have enabled the evolution of the crystallinity process to be measured. Commercial polyethylene films of M_w=90 000 were exposed in a weathering UV-chamber under known conditions of exposure time and radiant energy. The spectral profiles were modelled using Fourier methods. The relative amounts of the orthorrombic crystalline phase, α_c, the amorphous phase, α_a and the interphase, α_b, were calculated using Raman bands at 1416 cm⁻¹ characteristic of the crystalline phase and the bands at 1080, 1305 cm⁻¹, characteristic of the amorphous phase. The interphase content can be calculated from the relationship αb= 1-(α_c+α_a). It was found that the weathering process affects only the relative intensities of the bands attributed to crystalline and amorphous fractions; the crystalline content increases at the expenses of the amorphous fraction. These results are discussed in terms of the changes in the intermolecular forces caused by radiation exposure.