Glass transition of the two distinct single-chain particles of poly(N-isopropylacrylamide)

Two distinct single-chain particles of poly(N-isopropylacrylamide) (PNIPAM) in the state of loose coil and compact globule, have been prepared successfully below and above the lower critical solution temperature (LCST) in extreme dilute aqueous solution by the freeze-drying method, respectively. During the preparation of the compact globular single-chain sample, the surfactant of sodium n-dodecyl sulfate (SDS) was added into the system to prevent aggregation of globular single chains formed at a temperature above the LCST. After all the coil has been transformed into the compact globular particle, the SDS molecules were removed by dialysis. The glass transition temperature (T_g) of the two single-chain samples has been measured by differential scanning calorimetery (DSC) in comparison with that of bulk polymer. It was found that the T_g of the single-chain sample in compact-globule state was very near to that of the bulk polymer, whereas the T_g of the single-chain sample in loose-coil state was approximately 6 K lower than that of the bulk polymer. After treating the sample with repeated DSC cycles, the T_g of the single-chain sample in loose-coil state rose up successively near to that of the bulk polymer. These results have been explained in terms of the effect of entanglement on the mobility of the polymer segments in the two distinct single-chain samples.     

Frequency-dependent specific heat near the glass transition measured with the photoacoustic effect

For the supercooled salt melt 0.4 Ca(NO₃)₂–0.6 KNO₃ the photoacoustic amplitude and phase shift are measured in the glass transition region. The transition temperature is defined by the maximum in the phase angle. It is shifted to lower temperatures for lower frequencies. A frequency-dependent specific heat can be calculated from the data in the dispersion region. The frequency dependence of the transition temperature can be fitted by a power law with exponent =8.8±1.This work is part of a Ph. D. thesis at the Technische Universität München     

Apparent correlations between the static length of relaxation and the linear size of dynamic heterogeneity in fragile liquids

The most puzzling aspect of the glass transition observed in laboratory is the decoupling of the dynamics from the structure. As an attempt to reconcile the dynamic and the static lengthscales associated with the glass problem, we discuss the apparent correlations between the static relaxation length, defined as that lengthscale over which the potential energy fluctuation is correlated, with the linear size of the dynamic heterogeneity. The dynamic heterogeneous domains with long life-times, may therefore be linked to the droplets of low potential energy, or the tightly bound regions inside the liquid.     

Phase transition at 240 K in C70 single crystal

The thermal expansion of single- and polycrystalline C₇₀ is studied between 5 and 315K using an ultrahigh-resolution capacitance dilatometer. We observe a first-order phase transition in single crystalline C₇₀ at 240K and a transition at 280K in polycrystalline C₇₀. X-ray diffraction measurements at 300K show that the C₇₀ single crystal has fcc symmetry, whereas the polycrystalline sample is multiphase (fcc and hcp). The results are compared to thermal expansion measurements of solid C₆₀.     

Average coordination-number dependence of glass-transition temperature in Ge-In-Se chalcogenide glasses

Twenty-six glassy compositions, belonging to the Ge_xIn₆Se_94-x and Ge_xIn₁₂Se_88-x families of the Ge-In-Se system, were prepared from high purity constiment elements. Differential Scanning Calorimetry (DSC) measurements were carried out on these glasses. The DSC thermograms were used to determine the glass transition temperatures (T _g) for the compositions examined. TheT _g-composition dependence of the Ge_xIn₆Se_94-x family shows a minimum inT _g at a value of the average coordination number, r, equal to 2.4. For both families of the glasses examined, theT _g-r dependence displays maxima at r=2.75 and r=2.83 for Ge_xIn₆Se_94-x and Ge_xIn₁₂Se_88-x families, respectively. These results are interpreted by using the Phillips model of rigidity percolation and Chemically Ordered Covalent Network (COCN) model.     

The mean spherical model for charged hard spheres

The reduced mean electrostatic potential v(r) and the radial distribution functions gij(r) for a system of charged hard spheres of equal diameter are calculated from the solution of the mean spherical model equation given by Waisman and Lebowitz. An analytical solution is given for v(r) and the gij(r) are shown to be the sum of the Percus-Yevick uncharged hard-sphere distribution function and an electrostatic term. The correct qualitative behaviour of the mean potential is predicted at high concentrations but the radial distribution functions are only accurate for low valency electrolytes at high concentrations.     

Overlap properties and adsorption transition of two Hamiltonian paths

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems. Received 4 December 1998 and Received in final form 10 March 1999     

Ground state and glass transition of the RNA secondary structure

RNA molecules form a sequence-specific self-pairing pattern at low temperatures. We analyze this problem using a random pairing energy model as well as a random sequence model that includes a base stacking energy in favor of helix propagation. The free energy cost for separating a chain into two equal halves offers a quantitative measure of sequence specific pairing. In the low temperature glass phase, this quantity grows quadratically with the logarithm of the chain length, but it switches to a linear behavior of entropic origin in the high temperature molten phase. Transition between the two phases is continuous, with characteristics that resemble those of a disordered elastic manifold in two dimensions. For designed sequences, however, a power-law distribution of pairing energies on a coarse-grained level may be more appropriate. Extreme value statistics arguments then predict a power-law growth of the free energy cost to break a chain, in agreement with numerical simulations. Interestingly, the distribution of pairing distances in the ground state secondary structure follows a remarkable power-law with an exponent -4/3, independent of the specific assumptions for the base pairing energies.     

Topological jamming and the glass transition in a frustrated system

The relationship between extended structures, glassy dynamics and an underlying critical point is examined in the context of a lattice model of fluctuating lines. Monte Carlo simulations are used to construct an effective, coarse-grained dynamics for the “order parameter” near the critical point. Analysis of the effective dynamics reveals that the critical point is associated with diverging barriers leading to the observed Vogel-Fulcher divergence of the relaxation times. A direct connection is established between the presence of extended structures and the activated dynamics. Received 15 March 2002     

Density-correlator signatures of the vulcanization transition

Certain density correlators, measurable via various experimental techniques, are studied in the context of the vulcanization transition. It is shown that these correlators contain essential information about both the vulcanization transition and the emergent amorphous solid state. Contact is made with various physical ingredients that have featured in experimental studies of amorphous colloidal and gel systems and in theoretical studies of the glassy state. Received 30 September 2000     

Phase diagram of an Ising model with competitive interactions on a Husimi tree and its disordered counterpart

We consider an Ising competitive model defined over a triangular Husimi tree where loops, responsible for an explicit frustration, are even allowed. We first analyze the phase diagram of the model with fixed couplings in which a “gas of noninteracting dimers (or spin liquid) — ferro or antiferromagnetic ordered state” zero temperature transition is recognized in the frustrated regions. Then we introduce the disorder for studying the spin glass version of the model: the triangular ±J model. We find out that, for any finite value of the averaged couplings, the model exhibits always a finite temperature phase transition even in the frustrated regions, where the transition turns out to be a glassy transition. The analysis of the random model is done by applying a recently proposed method which allows us to derive the critical surface of a random model through a mapping with a corresponding nonrandom model.     

Some exact results on the ultrametric overlap distribution in mean field spin glass models (I)

The mean field spin glass model is analyzed by a combination of exact methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks.It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process.It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution.     

Dielectric relaxation of poly(ethylenglycol)- b-poly(propylenglycol)-b-poly(ethylenglycol) copolymers above the glass transition temperature

The complex dielectric permittivity has been measured for three poly(ethylenglycol)-b-poly(propylenglycol)-b-poly(ethylenglycol) copolymers with different content of poly(ethylenglycol) (15%, 33% and 80%), and increasing degree of crystallinity (0%, 10% and 20%, respectively). Only the non-crystalline sample shows the normal mode relaxation together with the segmental (α-relaxation) and the Johari-Goldstein (β-relaxation) modes. The crystalline samples show also polarization contributions due to the existence of interfaces between the crystallites and the amorphous phase. The relaxation times of the (α and normal modes can be described by a VFT equation with the same value of T₀. There is a slowing-down of the segmental mode due to the presence of crystallites. The temperature dependence of the α and β relaxations in the copolymers is very similar to that found in pure PPG, while there are significant differences in the case of the normal mode of the non-crystalline sample. The size of the cooperatively rearranging regions CRR, and the width of the glass transition region increase slightly with the degree of crystallinity. The temperature dependence of the size of CRRs is compatible with the prediction of fluctuation theory. No systematic effect of the degree of crystallinity on the β-relaxation has been found. Near T _g the β-relaxation time is close to the primitive time of the coupling model. Received: 31 May 2000     

The properties of free polymer surfaces and their influence on the glass transition temperature of thin polystyrene films

We present a detailed study of free polymer surfaces and their effects on the measured glass transition temperature (T_g) of thin polystyrene (PS) films. Direct measurements of the near-surface properties of PS films are made by monitoring the embedding of 10 and 20 nm diameter gold spheres into the surface of spin-cast PS films. At a temperature T = 378K( > T_g), the embedding of the spheres is driven by geometrical considerations arising from the wetting of the gold spheres by the PS. At temperatures below T_g ( 363K < T < 370K), both sets of spheres embed 3-4 nm into the PS films and stop. These studies suggest that a liquid-like surface layer exists in glassy PS films and also provide an estimate for the lower bound of the thickness of this layer of 3-4 nm. This qualitative idea is supported by a series of calculations based upon a previously developed theoretical model for the indentation of nanoscale spheres into linear viscoelastic materials. Comparing data with simulations shows that this surface layer has properties similar to those of a bulk sample of PS having a temperature of 374 K. Ellipsometric measurements of the T_g are also performed on thin spin-cast PS films with thicknesses in the range 8nm < h < 290nm. Measurements are performed on thin PS films that have been capped by thermally evaporating 5 nm thick metal (Au and Al) capping layers on top of the polymer. The measured T_g values (as well as polymer metal interface structure) in such samples depend on the metal used as the capping layer, and cast doubt on the general validity of using evaporative deposition to cover the free surface. We also prepared films that were capped by a new non-evaporative procedure. These films were shown to have a T_g that is the same as that of bulk PS (370±1 K) for all film thicknesses measured (> 7 nm). The subsequent removal of the metal layer from these films was shown to restore a thickness-dependent T_g in these samples that was essentially the same as that observed for uncapped PS films. An estimate of the thickness of the liquid-like surface layer was also extracted from the ellipsometry measurements and was found to be 5±1 nm. The combined ellipsometry and embedding studies provide strong evidence for the existence of a liquid-like surface layer in thin glassy PS films. They show that the presence of the free surface is an important parameter in determining the existence of T_g reductions in thin PS films.     

Surface glass transition in bimodal polystyrene mixtures

Using the cluster-embedding method of V. Zaporojchenko et al. (Macromolecules 34, 1125 (2000)), we measured the glass transition temperature T _g at the polystyrene/vacuum interface of bimodal mixtures of monodisperse polystyrenes of 3.5k and 1000k. Embedding of ≈ 1 nm Au clusters was monitored in situ by X-ray photoelectron spectroscopy (XPS). The clusters were formed by evaporation of Au onto the polymer surface. Only one glass transition was observed in the mixtures. The surface glass transition temperatures are correlated to but are below the bulk values of the mixtures and obey the Gordon-Taylor equation. The results suggest that the earlier reported molecular-weight dependence of the surface glass transition is not due to segregation of short chains to the surface.     

A quantum field theory of the liquid-glass transition in multi-component liquids

An established unified theory of the liquid-glass transition in one-component liquids is extended to multi-component liquids. The universal features such as the Kauzmann paradox, the Vogel-Tamman-Fulcher (VTF) law on the relaxation times and the transport coefficients, the jump of the specific heat at the glass transition temperature and the Boson peaks are elucidated. The Kauzmann entropy in a form of a Curie law with a negative sign comes from the mixing between the sound and the intra-band fluctuation entropies, where the critical temperature corresponds to the sound instability temperature at a reciprocal particle distance. The VTF law is constructed from the Einstein relation on entropy and probability so that the Kauzmann entropy is included as a normal form in exponent of the VTF law. The Kauzmann entropy explains the Kauzmann paradox and the jump of the specific heat so that the universal features of the glass transition are elucidated consistently.     

Dynamic-mechanical and nuclear magnetic resonance study of relaxation processes in ultra-high molecular weight polyethylene fibres

The relaxation processes (α, β, and γ) in UHMW PE fibres drawn to different draw ratios λ have been studied by dynamic-mechanical and nuclear magnetic resonance methods. The temperature dependences of tensile loss moduli E″ and spin-lattice relaxation times T ₁ have been analyzed assuming distribution of correlation times τ according to the Davidson—Cole function. The activation energies E _a and parameters ε characterizing widths of distribution, and asymptotic value τ ₀ for correlation times have been determined from experimental data for low-temperature γ-process and for high-temperature α-process. A weak β-process has been found by dynamic-mechanical method and quantitative analysis was made only for fibres with λ = 9. The temperature dependences of second moment M ₂ of the broad-line NMR spectra have been analyzed according to the Gutowsky—Pake formula, which includes only a single correlation time τ _c without distribution. In this case the activation energies E _a and values of τ ₀ have been determined.