Dielectric and molecular dynamics study of the secondary relaxations of poly(styrene-co-methylmethacrylate) copolymers: Influence of the molecular architecture

The effect of the structure of copolymers (random, alternate or diblock) on their dynamics has been studied by dielectric spectroscopy. Six copolymers of styrene and methyl methacrylate (three diblocks, one alternate and two random) have been studied. The results show that the sub- T _g transitions of the diblock samples can be described by one asymmetric Havriliak-Negami (HN) function, while two are necessary for the rest of the copolymers (β and γ relaxations). The characteristic times of the sub- T _g relaxations show an Arrhenius temperature dependence and there is a strong coupling of the α and β relaxations at high temperatures. The deconvolution of the merging relaxations has been made in the framework of the Williams Ansatz set out in terms of Havriliak-Negami distributions. Because the 2D ²H-NMR results excluded any significant contribution from the rotation of the methoxy group of the methacrylate group around the C-OCH₃ bond, the γ relaxation may be assigned to the rotation of the methyl methacrylate group in a styrene-rich environment. The Molecular Dynamics simulations of a poly(methyl methacrylate) homopolymer and of the alternate copolymer are in qualitative agreement with the experimental results, although they predict smaller values for the activation energy of the sub- T _g relaxations.     

Liquid–Liquid Transition and Detrapping of Trapped Carriers of P(MMA/BA) Copolymers by Thermally Stimulated Depolarization Current

Poly (methyl methacrylate/butyl acrylate) [P(MMA/BA)] copolymers (M _η～2×10⁵) with different mass percentages of PMMA (100/0, 90/10, 81/19, and 75/25), were synthesized by the method of solution polymerization. In addition to the normal α and ρ peak, a third τ peak is observed in thermally stimulated depolarization current (TSDC) spectra of the copolymers in the high temperature region. The α peak‐corresponds to the glass transition, the ρ peak originates from the detrapping of trapped carriers in the bulk amorphous structure related with flexible side groups, and the τ peak can be attributed to the charge detrapping related to the liquid–liquid transition of the copolymers. The three peaks all move to lower temperature with an increase of the BA component, indicating that the flexible side groups of butyl acrylate not only have an effect of plasticization on the glass transition and liquid–liquid transition, but also make the trap depth shallower and the detrapping process easier for the ρ and τ peaks. The experimental results confirm that TSDC analysis is very sensitive for investigating the liquid–liquid transition of polymers. The liquid–liquid transition temperature (T _LL) of the copolymers follows a type of the Fox equation. Fitting the results gives a T _LL of 102°C for polybutyl acrylate.     

Thermostimulated creep in amorphous polyolefins. II

The thermostimulated creep of three amorphous polyolefins having the repeating unit ─(CH₂)_mC(CH₃)(C₂ H₅)─, where m = 1, 2, and 3, was investigated from 77° K to 350° K. A broad relaxation process is observed around the glass transition temperature in each polyolefin. The corresponding TSC peaks have been resolved into elementary components with a relaxation time τ obeying a compensation law τ = τ_c exp {(ΔH/k)[1/T) —(1/T_c)], where T_c and T_c are characteristic of the polyolefin. From the TSC data, we have calculated, the mechanical loss peaks associated with the glass transition and we have compared them with the dielectric loss peaks.     

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model (RFIM) on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field (B). The random field (hi) is assumed to be Gaussian distributed with zero mean and a variance     

Transport of noble gases in poly(methyl acrylate)

The permeability, diffusivity, and solubility of He, Ne, Ar, and Kr were determined in poly(methyl acrylate) (PMA), in a temperature range encompassing the glass transition temperature, T_g. Activation energies for diffusion, E_D, were higher above Tg than below Tg for all four penetrants in PMA and in the structural isomer of PMA, poly(vinyl acetate) (PVA). For all penetrants studied, the Tg, the magnitude of the enthalpy of mixing (ΔH_m), as well as the E_D were all larger for PVA than for PMA. These differences were attributed to the stronger dipole-dipole interactions possible in PVA where the dipolar carbonyl group is separated from the chain backbone by an oxygen atom.

The carbonyl group in PMA is immediately adjacent and presumably sterically hindered by the chain backbone which suggests that PMA might be a stiffer molecule than PVA. Entropy considerations suggest that molecularly stiff polymers should be associated with small values of v Δα, ΔE_D, ΔE_D, ΔH_p, and (β), where v is the specific volume, Δα is the change in thermal expansivity about T_g, ΔH_p is the change in activation energy for diffusion about Tg, ΔE_D is the enthalpy of polymerization, and (β) is the logarithmic bulk relaxation rate constant of specific volume below T_g. These predictions appear to be satisfied for the systems of argon in PVC, PMA, PVA, and poly(ethyl methacrylate) (PEMA). The data suggest that PMA is a stiffer molecule than PVA. The weaker intermolecular forces of attraction and more hindered molecular rotations of PMA are consistent with a priori considerations of steric effects which have their origin in the fundamental structure of the PMA and PVA molecules.

The fraction of volume, φ, not occupied by polymer, estimated by several independent means for PMA at T_g, appears to be greater than that of PVA. Each of these two comparisons suggests that the molecular packing of PMA is more dense than the molecular packing of PVA.

The observed slow decrease in specific volume for PMA below Tg suggests that there could be regions throughout the polymer below Tg where the density is less than the equilibrium value. These predictions are consistent with the analyses of penetrant solubility below Tg which suggest that the molal volumes of the penetrants below Tg are larger than those above Tg. Also, analyses of the solubility data suggest that the enthalpies of mixing the noble gases in PMA tend to be exothermic below Tg. This suggests that below Tg, specific interactions occur between PMA and noble gas penetrants. The interactions are apparently manifested by decreases in free energy which are larger than expected for inert penetrants. The solubility and volumetric data appear to be consistent with the hypothesis that the polymer below Tg contains expanded, high-energy regions which preferentially absorb the diffusing penetrants.     

<Superscript>1</Superscript>H NMR study of molecular dynamics of acetylcholine chloride

The longitudinal relaxation timeT ₁ and the second momentM ₂ of¹H nuclear magnetic resonance line in a wide temperature range have been measured for acetylcholine chloride. Two different types of the methyl groups reorientation occurred. The first type was the hindered rotation of the methyl group denoted as C(1)H₃ about the threefold symmetry axis. The second type was the reorientation of the trimethyl group-N(CH₃)₃ around the pseudo C₃^′ axis of C(6)-N(7) bond, which accompanied the standard C₃ motion of the methyl group. The Dunn-McDowell model was applied to analyze the dynamics observed.     

Muon spin relaxation as a probe of molecular dynamics of organometallic compounds

LF‐Muon Spin Relaxation data are reported for the organometallic compounds Pb(C₆H₅)₄, (C₆H₆)Cr(CO)₃ and (C₅H₅)₂Ru. In each case the change in relaxation rate with temperature shows a peak analogous to the T_1 minimum in NMR. The activation parameters were calculated, and the mechanism of muon spin relaxation in the case of (C₆H₆)Cr(CO)₃ is shown to be the reorientation motion of the benzene ring. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ellipsometry measurements of glass transition breadth in bulk films of random, block, and gradient copolymers

Bulk films of random, block and gradient copolymer systems were studied using ellipsometry to demonstrate the applicability of the numerical differentiation technique pioneered by Kawana and Jones for studying the glass transition temperature (T _g) behavior and thermal expansivities of copolymers possessing different architectures and different levels of nanoheterogeneity. In a series of styrene/n -butyl methacrylate (S/nBMA) random copolymers, T _g breadths were observed to increase from ～ 17^° C in styrene-rich cases to almost 30^° C in nBMA-rich cases, reflecting previous observations of significant nanoheterogeneity in PnBMA homopolymers. The derivative technique also revealed for the first time a substantial increase in glassy-state expansivity with increasing nBMA content in S/nBMA random copolymers, from 1.4×10^-4 K-1 in PS to 3.5×10^-4 K-1 in PnBMA. The first characterization of block copolymer T _g ’s and T _g breadths by ellipsometry is given, examining the impact of nanophase-segregated copolymer structure on ellipsometric measurements of glass transition. The results show that, while the technique is effective in detecting the two T _g ’s expected in certain block copolymer systems, the details of the glass transition can become suppressed in ellipsometry measurements of a rubbery minor phase under conditions where the matrix is glassy; meanwhile, both transitions are easily discernible by differential scanning calorimetry. Finally, broad glass transition regions were measured in gradient copolymers, yielding in some cases extraordinary T _g breadths of 69- 71^° C , factors of 4-5 larger than the T _g breadths of related homopolymers and random copolymers. Surprisingly, one gradient copolymer demonstrated a slightly narrower T _g breadth than the S/nBMA random copolymers with the highest nBMA content. This highlights the fact that nanoheterogeneity relevant to the glass transition response in selected statistical copolymers can be comparable to or exceed that observed in moderately phase-segregated gradient copolymers.     

Density functional study of the cysteine adsorption on Au nanoclusters

The adsorption of the cysteine amino acid (H–SC_βH₂–C_αH–NH₂–COOH) on the Au₅₅ cluster is investigated through density functional theory calculations. Two isomers, with icosahedral (I_h) and chiral (C₁) geometries, of the Au₅₅ cluster are used to calculate the adsorption energy of the cysteine on different facets of these isomers. Results, only involving the S(thiolate)-Au bonding show that the higher adsorption energies are obtained when the sulfur atom is bonded to an asymmetrical bridge site at the facet containing Au atoms with the lowest coordination of the C₁ cluster isomer.     

Glassy behaviour of random field Ising spins on Bethe lattice in external magnetic field

The thermodynamics and the phase diagram of random field Ising model (RFIM) on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field (B). A Gaussian distribution of random field (hi) with zero mean and variance hi2 = HR2F is considered. The free-energy (F ), the magnetization (M) and the order parameter (q) are investigated for several values of coordination number (z). The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature TC = J/k and when HRF = 0 for finite z. The free-energy (F) values increase as T increases for different intensities of random field (HRF) and finite z. The internal energy (U) has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases. The ferromagnetic (FM)-paramagnetic (PM) phase boundary is clearly observed only when z →∞. While FM-PM-spin glass (SG) phase boundaries are present for finite z. The magnetic susceptibility (χ) shows a sharp cusp at TC in a small random field for finite z and rounded different peaks on increasing HRF.     

A structural phase transition in squaric acid

Squaric acid (3,4-dihydroxy-3-cyclobutene-1,2-dione) is found to undergo a second order antiferrodistortive tetragonal to monoclinic phase transition at 97.7°C. The transition temperature for the fully deuterated compound is 243°C. The crystals are optically biaxial negative at room temperature, and the partial birefringence decreases with temperature as (n_z ? n_y)α(T_C ? T)^β, where β_H = 0.34 ± 0.02 and β_D = 0.37 ± 0.04.     

Effect of chirality on the dynamics of domain walls in the molecular ferrimagnet [MnII(HL-pn)(H2O)][MnIII(CN)6] · 2H2O

The contributions from modes of switching, sliding, creep, and Debye relaxation of pinned domain walls to the low-frequency magnetic properties of the chiral and racemic molecular ferrimagnets [Mn^II(HL-pn)(H₂O)][Mn^III(CN)₆] · 2H₂O have been separated. It has been found that the chirality of the atomic and spin structures affects the temperatures of the transitions from the sliding mode to the creep mode and from the creep mode to the mode of Debye relaxation. In the chiral crystals, transitions to the creep and Debye relaxation modes have been observed at temperatures T = 7 and 5 K, respectively. In the racemic crystals, these transitions have been observed at temperatures T = 13 and 9 K, respectively, all other factors being equal.     

Microhardness of condensation polymers and copolymers. 1. Coreactive blends of polyethylene terephthalate and polycarbonates

The microhardness of coreactive blends of polyethylene terephthalate (PET) and bisphenol A polycarbonate (PC) was investigated over the whole range of compositions. The occurrence of one single glass transition temperature (T _g) step in the differential scanning calorimetry (DSC) curves indicated that intensive chemical interactions had taken place during melt blending, resulting in formation of copolycondensates with dominating random sequential order. The parallel decrease of microhardness (H) and of T_g with increasing PET content in the blends has been ascribed to the formation of new copolymer molecules enriched in the component characterized by lower H and T _g values. It is emphasized that such noncrystallizable copolymers offer the possibility to evaluate the intrinsic contribution of the repeating units to the H and T _g characteristics of copolymers with various compositions and sequential orders.     

Investigation of Pendant Group and Chain Segment Motions in P(MMA/BA) Copolymers by Thermally Stimulated Depolarization Current

Poly(methyl methacrylate/butyl acrylate) [P(MMA/BA)] copolymers (M_η ～2×10⁵) with different mass percentages of MMA were synthesized by the method of solution polymerization. Thermally stimulated depolarization current (TSDC) technique was used to investigate the effect of copolymerization on pendant group and chain segment motions. Three TSDC peaks were observed over the temperature range from 310 to 400 K. The highest temperature, ρ peak originates from the detrapping of trapped charge carriers. The lower temperature, α peak corresponds to the glass transition. The activation energy of the α relaxation decreases from 1.2 eV for PMMA to 0.98 eV for MMA(75)/BA(25). In the fitting process, another peak, β′, is separated on the low temperature side. The apparent energy barrier of the β′ for PMMA is 0.80 eV. The β′ relaxation is thought to correspond to the motion of pendant groups including intra‐ and inter‐molecular interactions. All three peaks move to lower temperatures with an increase in BA component, and the activation energy for the α and β′ relaxations also decreases with the increase of BA component in copolymers, indicating that the flexible side groups of BA have an effect of plasticization on the glass transition and motion of pendent groups. The temperatures of the α and β′ peaks of P(MMA/BA) copolymers follow the Fox equation. Fitting results gives the α peak at 238 K and β′ peak at 225 K for polybutyl acrylate (PBA).     

Alternating magneto-birefringence of ionic ferrofluids in crossed fields

A dynamic probing of magnetic liquids is performed experimentally, using a static magnetic field modulated by another smaller field, normal and alternating. The optical magneto-birefringence under these crossed magnetic fields is recorded as a function of the frequency for different field intensities and different sizes of the magnetic nanoparticles. A general reduced behavior is found for the in-phase and the out-of-phase optical response which is well-described by a simple mechanical model. Depending on the value H _ani of the anisotropy field of the nanoparticles, we can distinguish two different high magnetic field regimes: - a rigid dipole regime (large anisotropy energy with respect to k _B T) for cobalt ferrite nanoparticles with a relaxation time inversely proportional to the field intensity H _C(H _C < H _ani), - a soft dipole regime (anisotropy energy of the order of k _B T) for maghemite nanoparticles with a relaxation time independent of the field intensity H _C(H _C > H _ani). Received 5 June 2000 and Received in final form 8 January 2001     

Dielectric relaxation of α-cyclodextrin-polyiodide complexes (α-cyclodextrin)2 · BaI2 · I2 · 8H2O and (α-cyclodextrin)2 · KI3 · I2 · 8H2O

The frequency and temperature dependence of the real (ε′) and imaginary (ε″) parts of the dielectric constant of the polycrystalline complexes (α-CD)₂ · Bal₂ · I₂ · 8H₂O and (α-CD)₂ · KI₃ · I₂ · 8H₂O (α-CD = α-cyclodetrin) have been investigated over the frequency and temperature ranges 0–100 kHz and 120–300 K, respectively. The temperature dependences of ε′, ε″ and the phase shift φ show two steps, two peaks and two minima, respectively, revealing the existence of two kinds of water molecule, the tightly bound and the easily movable water molecules, in both complexes. The first peak of (T) or the first minimum of φ(T) presents the transformation of flip-flop hydrogen bonds to the normal state. The second ε″ (T) peak or φ(T) minimum corresponds to the easily movable water molecules or to a partial transformation of tightly bound to easily movable water molecules. For T > 270K both samples show semiconductive behaviour with energy gaps of 1.84eV for the (α-CD)₂ · BaI₂ · I₂ · 8H₂O complex and 1.36eV for the (α-CD)₂ · KI₃ · I₂ · 8H₂O complex. The conductivity at room temperature decreases in the order: (α-CD)₂ · BaI₂ · I₂ · 8H₂O > (α-CD)₂ · LiI₃ · I₂ · 8H₂O > (α-CD)₂ · KI₃ · I₂ · 8H₂O > (α-CD)₂ · Cd_0.5 · I₅ · 26H₂O. The relaxation time varies in a Λ-like curve (from 120 to 250 K) and rises rapidly for temperatures greater than 250 K, indicating the process of ionic movements. The activation energies around the transition temperature 0.98–1.09 k _B T _trans for (α-CD)₂ · BaI₂ · I₂ · 8H₂O and 1.06-1.55 k _B T _trans for (α-CD)₂ · KI₃ · I₂ · 8H₂O reveal the greater stability of the α-K complex against that of the α-Ba complex.     

Spin-lattice relaxation in 13CH3 compounds: application to 13C enriched aspirin

Spin-lattice relaxation processes in ¹³CH₃ groups in methyl compounds are studied both theoretically and experimentally. The four spin-½ nuclei in such methyl groups give rise to 16 spin-rotational states, which are split by rotational tunnelling. From the corresponding populations (15 independent) five long lived combinations are formed: the ¹³C magnetization M _C, proton magnetization M _H, tunnelling energy TE, rotational polarization RP and dipolar energy DE. Their spin-lattice relaxation via the transitions induced by the ¹³C-proton dipolar interaction is studied in detail. Direct relaxation rates and coupling terms between these combinations are derived. Predictions are compared with experimental data for ¹³C spin-lattice relaxation at 75.4 MHz in 99% enriched (only methyl carbons enriched) single crystal of aspirin. Above 40 K, the M _C recovery is exponential and describable in terms of the direct relaxation transitions without couplings. The same is true for the initial relaxation in the region of non-exponential relaxation between 30 K and 40 K. The orientation dependence of the initial relaxation rate agrees with the theoretical calculations. The non-exponentiality is related to resonant level-crossing transitions with ω_t, + ω_C = ω_H, where the angular frequencies represent rotational tunnelling and carbon and proton resonances, respectively. The resonant transitions produce couplings between M _C, M _H and TE that are described quite accurately by the present model.     

NMR relaxation study of disorder in the mixed system BP x GPI(1–x) and the low temperature transition from classical to quantum rotation

¹H NMR spin-lattice relaxation time (T ₁) studies have been carried out in the temperature range 100 K to 4 K, at two Larmor frequencies 11.4 and 23.3 MHz, in the mixed system of betaine phosphate and glycine phosphite (BP_xGPI_(1–x)), to study the effects of disorder on the proton group dynamics. Analysis of T ₁ data indicates the presence of a number of inequivalent methyl groups and a gradual transition from classical reorientations to quantum tunneling rotations. At lower temperatures, microstructural disorder in the local environments of the methyl groups, result in a distribution in the activation energy (E_a ) and the torsional energy gap (E ₀₁). For certain values of x, the magnetisation recovery shows biexponential behaviour at lower temperatures.     

Spin-lattice relaxation in multiple-pulse experiments as contrast parameter in NMR imaging of solids

The molecular motion contrast parameter for NMR imaging of solids and quasi-solids based on the spin-lattice relaxation (T _leff) in multiple-pulse experiments is discussed. For Ostroff-Waugh multiple-pulse sequence theT _leff contrast parameter is evaluated in slow and fast molecular motion regime and compared with spin-lattice relaxation in the rotating frame contrast parameter. It is shown thatT _leff is offering a good molecular motion contrast in NMR imaging of polymer systems. The radio-frequency pulse scheme forT _leff-imaging using magic-echo phase-encoding procedure for recording spatial distribution in solids is introduced. A method forT _leff-weighted imaging using gradient spin-echo valid for weak dipolar solids is also discussed. The one-dimensional protonT _leff image using Ostroff-Waugh pulse sequence in combination with frequency-encoding imaging procedure is presented for a phantom of poly(ethyleneoxide) and poly(methylmethacrylate). The distribution of mechanical stresses in a acrylate film on glass is investigated by protonT _leff-imaging. A proton spin-density image weighted byT _leff, for a mixture of two elastomers with different crosslink density is also shown.