Anisotropy of local relaxation properties of macromolecules. Spin-lattice relaxation of 13C nuclei,the nuclear overhauser effect and the estimation of parameters of an equivalent ellipsoid for kinetic segments of polymer chains

The expressions for the functions of spectral density at different orientations of the components of the internuclear vector with respect to the chain backbone, the frequency dependences of the spin-lattice relaxation time of ¹³C nuclei (T_1C) and the values of the nuclear Overhauser effect (NOE) were obtained for the tetrahedral lattice model of a polymer chain with three-unit kinetic elements. It was shown that peculiar features of the behavior of T_1C and NOE reflect the characteristic properties of the spectra of relaxation (correlation) times for “longitudinal” and “transverse” components of the internuclear vector. It was established that in the range of relatively short times of the relaxation spectrum the dynamics of an anisotropic kinetic segment of the chain may be described with the aid of a simple model of an elongated ellipsoid of rotation with an axial ratio of about 10. It is shown that the equivalent-ellipsoid model leads to significant differences from a more specific model of chain dynamics when a broad frequency range is considered.     

Pressure dependence of the β molecular relaxation process and dielectric properties of polyvinylidene fluoride

The effects of hydrostatic pressure to 20 kbar on the β molecular relaxation process of polyvinylidene fluoride (PVDF) and on the dielectric properties in the neighborhood of this relaxation have been investigated. This relaxation has a strong influence on the electrical and mechanical properties of PVDF. Pressure causes a large shift to higher temperatures (～ 10K/kbar) of the dielectric relaxation peak and a decrease in the width of the distribution of relaxation times. This slowing down of the relaxation process is discussed in terms of the Vogel–Fulcher equation and related models, and it results from an increase in both the energy barrier to dipolar motion and the reference temperature (T₀) for the kinetic relaxation process which represents the “static” dipolar freezing temperature for the process. The general applicability of the Vogel–Fulcher equation to relaxional processes in polymers and other systems is briefly discussed. The pressure dependence of the dielectric constant both above and below the relaxation peak temperature (T_max) is found to be dominated by the change in polarizability. The effect is larger above T_max because of the relatively large decrease in the dipolar orientational polarizability with pressure.     

Dielectric and conductivity relaxations in poly(hema) and of water in its hydrogel

The dielectric permittivity ε′ and loss ε″ of anhydrous poly(2-hydroxyethyl methacrylate) and its 38.6 w/w% hydrogel have been measured in the frequency range from 12 Hz to 200 kHz and the temperature range from 77 to 273 K. The former has a sub-T_g relaxation with a half-width of 4.5 decades for the loss spectra, whose strength increases with temperature, and an activation energy of 62.5 kJ/mol. The dielectric relaxation time of the α process of supercooled water in the hydrogel is 53 s at its calorimetric T_g of 135 K. The half-width of the relaxation spectrum is 2.85 decades and, in the narrow temperature range, its apparent activation energy is 60.8 kJ/mol. Heating of the hydrogel causes crystallization of water which begins at about 207 K and becomes readily detectable as a second dielectric loss peak at about 230 K. For each temperature between 207 and 267 K, supercooled water in the hydrogel coexists with its crystallized form, with the amount of the crystallized solid increasing with increasing temperature. These results are discussed in terms of “bound” and “free” states of water in the hydrogel.     

Relaxations of thermosets. III. Sub-Tg dielectric relaxations of bisphenol-A–based epoxide cured with different cross-linking agents

The sub-T_g relaxations of bisphenol-A–based thermosets cured with diaminodiphenyl methane and diaminodiphenyl sulfone have been studied by dielectric measurements over the frequency range 12 Hz to 200 kHz from their ungelled or “least” cured states to their fully cured states. Both thermosets show two relaxation processes, γ and β, as the temperature is increased toward their T_gs. In the ungelled states, the γ process is more prominent than the β process. As curing proceeds, the strength of the γ process decreases and reaches a limiting value, while that of the β process initially increases, reaches a maximum value, and then decreases. An increase in the chain iength and the number of crosslinks increases the number of -OH dipoles and/or degree of their motions in local regions of the network matrix. This is partly caused by the decreasing efficiency of segmental packing as the curing proceeds. The sub-T_g relaxations become increasingly more, separated from the α relaxation during curing. Physical aging causes a decrease in the strength of the β relaxation of the thermosets as a result of the collapse of loosely packed regions of low cross-linking density, and this decrease competes against an increase caused by further crosslinking during the “post-cure” process.     

Micro‐rheology and relaxation phenomena in Tg vicinity

The present paper describes possible forms of relaxation phenomena in T_g vicinity. The individual types of relaxation in amorphous matrix are described in the areas of Vogel's temperature, T_g and crossover temperature. Special emphasis is laid on the difference between Flory's relaxation mechanism and the approach by Di Marzio, Adams and Gibbs. These authors used the common formula of Flory, however, their interpretations of the so‐called “configurational phenomena” reflect completely different realities. The theoretical justification of heat capacity as a complex number (recently introduced by Hutchinson, Monserrat and Schawe in T_g vicinity) is provided in detail and compared with the existing experimental evidence quoted by the authors of these contributions as well as with data published in literature. The relation between complex heat capacity and relaxation of internal stress in amorphous matrixes or the effects of ageing are discussed.     

Glass Transition Temperature and Value of the Relaxation Time at Tg in Vitreous Polymers

Summary: Many works focused on glassy polymers determine values of glass transition temperature (T_g) and an overview of the literature shows that depending on the method used, values of T_g are found different for the same material. In this paper, a review of data collected on different materials are used and interpreted in term of molecular mobility characterized by relaxation time functions. By using three independent experimental procedures (dielectric, thermally depolarized current and calorimetric), we show that the value of the glass transition and the value of the relaxation time at T_g can be correctly determined. It is also shown that the assumption: τ _(Tg) = 100 s is constant, is not correct. The protocol proposed also allows the determination of the value of the fragility index “m” of the glass forming liquid with a great accuracy.     

The Flipping of CO Ligand Groups in Metal Carbonyl Compounds and its Frequency in Fe(CO)5

It has been proven qualitatively by a number of authors using variable temperature NMR experiments that most metal carbonyl complexes are nonrigid. A quantitative determination of the ligand exchange frequency v_e is often achieved by a line shape analysis or by measurement of the transverse relaxation time T₂ using the Carr-Purcell method. In the case of a “very fast” exchange, however, both methods prove unsuccessful. It is shown in this study that a simultaneous fit of IR or Raman spectra on the one hand and NMR spectra on the other can make possible the determination of v_e for the “very fast” exchange and can also facilitate the determination of v_e in “slow” and “medium” exchange cases considerably. The ligand exchange frequency thus found for Fe(CO)₅, 1.1 × 10¹⁰s^?1, is unexpectedly high; comparison with variable temperature measurements on solid Fe(CO)₅, yields similar energy barriers. A mechanism of exchange closely related to the “Berry mechanism” is proposed. Finally the consequences of this surprisingly large ligand exchange rate are discussed with respect to IR band assignments for molecular “fragments” M(CO)^x (where x=coordination number, and M is a transition metal, typically lanthanoid or actinoid).     

Thermal relaxation of poled non-linear optical sidechain polymers: A new,semi-empirical model

Electro-Optic relaxation of a poled, Non-Linear Optical sidechain polymer with T_g 140°C, containing 4-dimethylamino-4′-nitrostilbene (“DANS”) in the sidechains, has been studied at 120°C with and without annealing at the same temperature. The time-dependence of the decaying EO coefficients r(t) shows a strong departure from the classical single-exponential Debye model, especially in the unannealed samples. This departure is attributed to physical ageing, slowing down the orientational relaxation of the sidechains. The Debye model with r(t)-r(0). exp -t/τ] is modified semi-empirically by introducing a time-dependent characteristic Debye relaxation time τ(t). Of several trial expressions, one is selected which fits the relaxation data. This is τ(τ)-τ_i+C.t^b     

Kinetics of structural relaxation of poly(ethylene terephthalate)

The results of an experimental study of the kinetics of structural relaxation of amorphous poly(ethylene terephthalate) are reported. Samples were prepared by ultraquenching the melt on rotating stainless-steel discs. Two types of measurements by differential scanning calorimetry were made: (1) the dependence of the “fictive” (or “structural”) temperature T_f(q^?) introduced by Tool, on the cooling rate q^? and (2) the dependence of the glass transition temperature T_g on the heating rate q⁺. In this way the value x = 0.47 was obtained for the dimensionless parameter proposed by Narayanaswamy.     

Statistics of stiff polymer chains near an adsorbing surface

The exact solution of the problem of adsorption of a long ideal polymer chain with variable degree of stiffness on a plane surface is presented. It is shown that the adsorption of stiff polymer chains is a second-order phase transition; in the adsorbed state “train” (i.e. adsorbed) sections are relatively longer and loop sections relatively shorter than for flexible chains. This effect is very pronounced: already for moderately stiff chains the number of Kuhn segment lengths in one “train” section at the temperature T = T_cr/2 (T_cr is the critical temperature for adsorption transition) can reach several thousands, and deviation from the surface occurs only in the form of small “hairpins”. The maximum length of the chain, which at the given conditions would flatten completely on the surface, is estimated.     

Light scattering and dielectric relaxation studies of glass forming liquids

Extended Abstract: Glass forming organic liquids and polymers exhibit long range density fluctuations with correlation length ξ in the range of 10–300 nm at temperatures above T_g (1 - 6). This follows from dynamic and static light scattering experiments revealing some unexpected features, which cannot be explained on the basis of conventional liquid state theories: (i) In static light scattering the intensity I(q → 0) is no longer proportional to the isothermal compressibility, (ii) This excess scattering I_exc shows a strong q-dependence (q = (4π/Λ.)sin(θ/2)) corresponding to a correlation length ξ in the above mentioned range, (iii) The Landau-Placzek ratio I_Rayleigh/2I_Brillouin is much too high compared with the results of light scattering theories, (iv) In photon correlation spectroscopy a new ultraslow hydrodynamic mode (Γ ˜ q²) is detected with relaxation rates Γ about 10⁻⁶ to 10⁻⁹ lower than those of the α-process at a given temperature. In order to explain these observations, a two-state fluid model is proposed, which starts from the coexistence of “liquid-like” and “aperiodic solid-like” regions within the liquids. Such ideas have been discussed many times before, so for example A.R. Ubbelohde (7) speculates about “anticrystalline” clusters in liquids. Molecular dynamics simulations of atomic liquids showed that long range orientational fluctuations appear upon supercooling (8). A preferred icosahedral ordering is observed (9) and the number of icosahedral clusters increases with decreasing temperature (10). In connection with the interpretation of the dynamics of supercooled liquids different “two-state” models have been proposed (11 - 15). For the explanation of the light scattering results we propose that the molecules in the different dynamic states (“liquid” or “solid”) aggregate during annealing of the liquid at temperatures above T_g. Experiments showed that the equilibration times can be rather long (3 - 5), but nevertheless the liquids exhibiting long range density fluctuations are in the state of lowest free energy. We claim that our observations are the first experimental proof of the existence of such different dynamic states, which have been discussed many times before. The extended secondary clusters can also be detected by ultra small angle X-ray scattering.     

Variable temperature 19F solid‐state NMR study of the effect of electrostatic interactions on thermally‐stimulated molecular motions in perfluorosulfonate ionomers

This study uses variable temperature ¹⁹F solid‐state nuclear magnetic resonance (SSNMR) spectroscopy to determine the influence of electrostatic interactions on the T₁, T_1ρ, and T₂ values of Nafion®. Because of a “homogenizing” of the T₁'s as a result of spin diffusion, it was not possible to resolve from the T₁ experiments the relative motions of the side‐ and main‐chain. The initial increase in T_1ρ as a function of increasing temperature has been attributed to backbone rotations that increase with increasing temperature. The maxima observed in the T_1ρ plots suggest a change in the dominant relaxation mechanism at that temperature. The similarity in relaxation behavior of the side‐ and main‐chains suggests that the motions are dynamically coupled, because of the fact that the side‐chain is directly attached to the main‐chain. Two T_1ρ values were observed for the main‐chain at high temperatures, which has been attributed to a thermally activated ion‐hopping process. The results of T₂ studies show that correlated motions of the side‐ and main‐chain exist at low temperatures. However, at elevated temperatures the T₂ values for the side‐chain increase rapidly while remaining relatively constant for the main‐chain, indicating an onset of mobility of the side‐chains. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2177–2186, 2007     

Self-nucleation and recrystallization of isotactic polypropylene (α phase) investigated by differential scanning calorimetry

The crystallization behavior after partial or complete melting of the α phase of iPP is examined by combined differential scanning calorimetry (DSC) and optical microscopy: calorimetric results are directly correlated with corresponding morphologies of microtome sections of DSC samples. On partial melting at various temperatures (hereafter referred to as T_s) located in a narrow range (4°C) below and near T_m, the number of nuclei increases (as in classical self-nucleation experiments), by several orders of magnitude; on subsequent cooling, the crystallization peak is shifted by up to 25°C. After partial melting in the lower part of the T_s range and recrystallization, the polymers display a prominent morphology “memory effect” whereby a phantom pattern of the initial spherulite morphology is maintained. After partial melting in the upper part of the T_s range the initial morphology is erased and self-nucleation affects only the total number of nuclei. The present experimental procedures make it possible to define, under “standard” conditions, the crystallization range of the polymer and in particular, the maximum crystallization temperature achievable when “ideally” nucleated. © John Wiley & Sons, Inc.     

Proton spin-lattice and spin-spin relaxation times in isotactic polypropylene—III. Effects of molecular weight

Proton spin-lattice (T₁) and spin-spin (T₂) relaxation times of isotactic polypropylene (molecular weights from 1.95 × 10⁵ to 1.78 × 10⁶) were measured at 40° using a wide line pulsed spectrometer operating at 19.8 MHz. Two series of samples with different thermal histories were prepared viz. a “melt-quenched sample” and an “annealed sample”. For all samples two T₁'s, the longer (T₁₁) and the shorter (T_1s), were observed. T₁₁ and T_1s decrease with increasing molecular weight. On the other hand, T_2a the longest T₂, associated with the most mobile amorphous region, increases with increasing molecular weight. The mass fraction of the rigid crystalline region decreases and those of the intermediate and mobile amorphous regions increase with increasing molecular weight. T₁₁ changes approximately linearly with the mass fraction of the crystalline region in the “melt-quenched sample”.     

Dielectric and Magnetic Relaxations Exhibited in a 2D Parallel Interpenetrating Frustrated Star Net

Constructing multiple functional geometric frustration magnets is a hot topic in solid state chemistry and material science. Herein, a two-dimensional (2D) parallel interpenetrating “star” net complex [HDMPDA][Fe₆(μ₃-O)₂(μ-O₂CH)₁₅] ( 1 ) was obtained successfully with HDMPDA (DMPDA=N, N’-dimethyl-1,3-propanediamine) as charge balancer. The dipole reorientation of the rotator [HDMPDA]⁺ in the complex brings a structure transition which leads dielectric relaxation close to room temperature. Despite strong antiferromagnetic coupling existing between ions in the net, long-range order temperature T_N of the complex is suppressed to 4.2 K by geometric frustration. Interestingly, below T_N, a canted antiferromagnetic state, accompanied with slow magnetic relaxation, is detected due to the lack of enough magnetic coupling between 2D layers. Thus, 1 is a particular multifunctional magnetic frustration material containing two different types of relaxations.     

Backbone dynamics of proteins studied by two-dimensional heteronuclear NMR spectroscopy and molecular dynamics simulations

To investigate the backbone dynamics of proteins ¹⁵N longitudinal and transverse relaxation experiments combined with {¹H, ¹⁵N{ NOE measurements together with molecular dynamics simulations were carried out using ribonuclease T₁ and the complex of ribonuclease T₁ with 2′GMP as a model protein. The intensity decay of individual amide cross peaks in a series of (¹H, ¹⁵N)HSQC spectra with appropriate relaxation periods was fitted to a single exponential by using a simplex algorithm in order to obtain ¹⁵N T₁ and T₂ relaxation times. The relaxation times were analyzed in terms of the “model-free” approach introduced by Lipari and Szabo. In addition, a nanosecond molecular dynamics (MD ) simulation of ribonuclease T₁ and its 2′GMP complex in water was carried out. The angular reorientations of the backbone amide groups were classified with several coordinate frames following a transformation of NH vector trajectories. In this study, NH librations and backbone dihedral angle fluctuations were distinguished. The NH bond librations were found to be similar for all amides as characterized by correlation times of librational motions in a subpicosecond scale. The angular amplitudes of these motions were found to be about 10°–12° for out-of-plane displacements and 3°–5° for the in-plane displacement. The contributions from the much slower backbone dihedral angle fluctuations strongly depend on the secondary structure. The dependence of the amplitude of local motion on the residue location in the backbone is in good agreement with the results of NMR relaxation measurements and the X-ray data. The protein dynamics is characterized by a highly restricted local motion of those parts of the backbone with defined secondary structure as well as by a high flexibility in loop regions. Comparison of the MD and NMR data of the free liganded enzyme ribonuclease T₁ clearly indicates a restriction of the mobility within certain regions of the backbone upon inhibitor binding. © 1996 John Wiley & Sons, Inc.     

Effect of crosslink length on the enthalpy relaxation of fully cured epoxy–diamine resins

Enthalpy relaxation of epoxy–diamine thermosets of different crosslink lengths (CLL) has been studied by DSC. The epoxy resins based on diglycidyl ether of bisphenol A were cured with ethylenediamine (FEDA), and diamines of polyoxypropylene of 2.6 and 5.6 oxypropylene units, named FJ230 and FJ400, respectively. As was expected, increasing the CLL decreases the glass transition temperature T_g from 121°C (FEDA) to 47°C (FJ400). Aging experiments at T_g − 20 K for each resin permit the determination of the enthalpy loss, the relaxation rate per decade (β_H), and the nonlinearity parameter, x. The apparent activation energy, Δh*, and the nonexponentiality parameter β are found for each resin from intrinsic cycles in which the sample is heated at 10 K min⁻¹ following cooling at various rates through the glass transition region. An increase of CLL is related to an increase of β_H, and of the nonlinearity parameter. In agreement with the general trend for thermoplastic polymers, the increase of the parameter x is correlated with a decrease of Δh* and with an increase in the nonexponentiality parameter. Application of the Adam–Gibbs (AG) theory reveals that the parameters B and T_f/T₂ increase with CLL, corresponding to a decrease of the nonlinear behavior of the glassy epoxies. However, the T₂ values calculated in this way appear unrealistic, and the alternative assumption that T₂ = T_g −51.6 K, making use of the “universal” WLF constant, leads to a much smaller variation of B, which nevertheless still increases with CLL. From a consideration of the minimum number of configurations required for a cooperative rearrangement, it is argued that the elementary activation energy Δμ increases, and the minimum size of the cooperatively rearranging region decreases as CLL increases. This is consistent with the relaxation process becoming more cooperative as the CLL decreases, as is suggested by the decrease in the value of β. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 456–468, 2000     

Microkinetics of crystallization in poly(ethylene terephthalate)

The lamellar growth kinetics and lamellar thickness of poly(ethylene terephthalate) crystallized from the glassy state have been determined as a function of crystallization temperature. Values of end and side surface free energies have been estimated as well as the residual lamellar thickness. Analyses carried out using secondary nucleation approaches indicate that the width of a critical nucleus is comparable to the effective substrate length for multiple nucleation in this and other slowly crystallizing polymers at high supercoolings. A “universal” critical value of T/T²ΔT below which the strip completion process ceases was found to exist. All crystallization must, therefore, occur through the deposition of critical nuclei. Models are proposed for this process which appear to be consistent with both neutron scattering and infrared experiments on quenched polyethylenes. Comparison of crystallization rates, expressed as “jump” rates, with relaxation frequencies suggest that in order for crystallization to occur at any given temperature the relaxation frequency must be at least two decades faster than the crystal “jump” rate.     

Crystallization of poly(aryl ether ketone ketone) copolymers containing terephthalate/isophthalate moieties

In a previous study, we have investigated the structure, crystallization, and morphology of poly(aryl ether ketone ketone), PEKK, copolymers prepared from diphenyl ether (DPE), terephthalic acid (T), and isophthalic acid (I) with T/I ratios from 100/0 to 50/50. These materials were considered as having -DPE-T-DPE-T- (TT) and/or -DPE-T-DPE-I- (TI) “phthalate diads.” In this work, we continue the study of this copolymer series with six different T/I ratios (40/60, 30/70, 20/80, 15/85, 10/90, and 0/100), which are viewed as having TI and/or -DPE-I-DPE-I- (II) “diads.” The I moieties (1,3-linked isomers) were always found to be incorporated in the crystals and acted as “entropy or symmetry” defects that effectively decreased the equilibrium melting temperature T_m^o and the rate of crystallization. However, the retardation of crystallization in PEKK 0/100 (the homopolymer with pure II diads) was significantly less than expected, which was attributed to the segregation of I moieties between the chains leading to a reduction of total entropy in the unit cells. The evidence of segmental segregation in PEKK 0/100 was seen in x-ray diffraction patterns, where several extra reflections were seen that could only be indexed by the published unit cell modified with a larger c-axis dimension (3.048 nm, corresponding to the length of six phenyl residues or 1.524 nm, the length of three phenyl residues). The composition of 15/85 was found to have the lowest value of T_m^o and the slowest crystallization rate. Upon heating, the “II” crystals (T/I from 30/70 to 0/100) exhibited the conventional double-melting behavior rather than the triple-melting behavior as in the “TI” crystals (50/50 to 40/60). No indication of the second polymorph form 2 was found in “II” crystals. © 1994 John Wiley & Sons, Inc.