An upper limit to kinetic fragility in glass-forming liquids

The kinetic fragility of a liquid is correlated to the magnitude of enthalpy hysteresis in various glass-forming materials during thermal cycling across the glass transition. While the lower bound of liquid fragility is well known, there has been little research into the possibility of an inherent upper limit to fragility. In this paper, we present a theoretical argument for the existence of a maximum fragility and show that the correlation between fragility and enthalpy hysteresis allows for an empirical evaluation of the upper limit of fragility. This upper limit occurs as the enthalpy hysteresis involved in thermal cycling about the glass transition approaches zero, leading to m(max)≈175. This result agrees remarkably well with our previous estimate. The dynamics of maximum fragility liquids are discussed, and a critical temperature of ～1.5 T(g) (where T(g) is the glass transition temperature) is revealed where a transition from nonexponential to exponential structural relaxation occurs.     

The dynamics of glass-forming polymers in the microscopic-mesoscopic time scale. A quasielastic neutron scattering phenomenological approach

The dynamics of three glass-forming polymers, PVC, PB and PI, has been investigated by time of flight (TOF) neutron scattering in a time scale from 10⁻¹³s to 10¹¹s looking for the crossover from microscopic dynamics to segmental dynamics (α relaxation). A new analysis procedure has been applied to TOF data in order to separate harmonic vibrational and relaxational contributions. Due to the involved assumptions, this procedure can be considered only as a first approximation adequate for the case of “fragile” systems (in the Angell's meaning) like the polymers here investigated. The behaviour obtained was the same for the three polymers studied. The intermediate scattering function corresponding to the relaxational dynamics, I_o(Q,t), shows two different dynamical regimes separated by a crossover time t_c (≈ 2 ps), which hardly depends on Q (momentum transfer) and temperature. At t < t<_c, I_o(Q,t) displays a Debye-like behaviour (exponential decay). The activation energy found for the relaxation time corresponding to this regime was in the range of 2–5 Kcal/mol, i.e., in the range of the activation energy for local conformational transitions in isolated macromolecular chains. At t > t_c and, at least at high temperature, I_o(Q,t) shows a Kohlrausch-Williams-Watts (KWW) behaviour similar to the obtained one by means of backscattering neutron techniques in the mesoscopic time scale (10⁻¹¹s to 10⁻⁷s) and dielectric measurements in the macroscopic time scale (10⁻⁷s to 10°s). This KWW regime can be associated to the segmental dynamics involved in the α relaxation. A phenomenological interpretation is outlined. In this framework, the Debye-like regime is interpreted to be the segmental dynamics free from intermolecular hindrances. Therefore, t_c should be the time at which intermolecular interactions start to play a significant role concerning to the segmental dynamics. This interpretation recalls some of the basic ideas of the so called “Coupling-Model” proposed a long time ago by Ngai.     

Improved calorimetric procedure for monitoring the approach to thermodynamic equilibrium in glassy polymers

Techniques for measuring the enthalpy change during isothermal aging of polymer glasses are discussed. Critical analysis of conventional scanning calorimetry reveals that its accuracy may be suspect under certain circumstances due to the thermal lag inherent in a temperature scanning experiment. An additional problem is that the conventional technique is restricted to certain kinds of paths for reaching the aging temperature. It is proposed that both problems can be overcome by analyzing the output of a scanning calorimeter not only during steady heating but also during the transients at the beginning and end of a heating scan. This data analysis method represents an extension of a method used previously by others in accurate measurements of the much larger heat of fusion of crystalline polymers. Practical feasibility of the improved technique is demonstrated by preliminary measurements of enthalpy relaxation during aging of well-characterized polystyrene at 80°C. In particular, the initial departure from equilibrium of a glass prepared by 5°C/min cooling from the liquid state is found to be 6.9 ± 0.6 J/g. This measured value agrees with a value calculated on the basis of the glass transition temperature corresponding to 5°C/min cooling and heat-capacity data from the literature.     

The impact of the stretching exponent on fragility of glass-forming liquids

The paper compared two factors governing fragility. The first one is thermodynamic, depending on the change in configurational entropy. The second one is kinetic and is determined by the stretching exponent β. Using a simple mathematical development, we show that the kinetic term \(m_{\text{K}} = f( {\beta_{{T_{\text{g}} }} } )\partial \ln \beta \left( T \right)/\partial \ln T|_{{T = T_{\text{g}} }}\) is always smaller than 1, where T _g is the glass transition temperature and \(f( {\beta_{{T_{\text{g}} }} } )\) is the given functions of the stretching exponent at T = T _g. As a result, the contribution of the kinetic term on the fragility of strong glasses is <6 %. Fragile glasses have a larger value of fragility index m, and for them, the influence of the kinetic term is significantly smaller. In any case, the thermodynamic term plays the main role in fragility and the kinetic one can be neglected.     

A synergistic approach to the polydispersity of polymers

A scheme for calculating polydispersity coefficients of polymers during chain propagation in living polymerization is proposed on the basis of the synergistic approach (the master equation) with allowance for fluctuations in the number of free radicals at the stage of initiation. The molecular-mass-distribution function of living chains is calculated. The form of this function is shown to be dependent on the ratio between the constants of the elementary stages of chain initiation and propagation.     

A thermodynamic approach to the stress-induced crystallization in cross-linked rubbers

The thermodynamic treatment of crystallization phenomena in a prestretched rubber was undertaken. Emphasis was put on defining conditions for the thermodynamic stability of the extendedor folded-chain crystal structure. The extended-chain structure is found to be stable thermodynamically at temperatures higher than the isotropic melting point of un-cross-linked polymer T in the stretched state, while the folded chain one is not. Below T, the stretch ratio of the network structure determines which crystal structure is more stable. The relation among the critical stretch ratio for the extended/folded crystalline structure transition, temperature, and molecular weight is also discussed. The crystallinity predicted by this work becomes zero at a temperature of T, the isotropic melting point of a cross-linked system. The value of T decreases with increasing cross-link density, and this is consistent with the experimental data reported in the literature.     

A modular approach to main-chain organometallic polymers

A highly efficient route to a new class of organometallic polymers containing difunctional N-heterocyclic carbenes has been developed. Bis(imidazolium) halides and divalent group X metals were copolymerized to afford organometallic polymers in up to quantitative yields and with molecular weights up to 10(6) Da, depending on the structure of the N-heterocyclic carbene and the incorporated transition metal. Enhanced solubilities were demonstrated through post-polymerization ligation with phosphines. Finally, selective end-group functionalization and excellent molecular weight control was achieved through the inclusion of monofunctional chain transfer agents during the polymerization.     

Cooperative rearranging regions in polymeric materials: Relationship with the fragility of glass-forming liquids

From measurements performed on different polymeric glass-forming liquids using differential scanning calorimetry (DSC), we determined the values of the fragility index m according to the concept proposed by Angell. We calculated the average size of a cooperative rearranging region (CRR) at the glass transition i.e. z(T_g), according to the definition proposed by Solunov. This quantity is linked to the Kauzmann temperature which was determined from dielectric spectroscopy or viscosimetry measurements performed on different samples including three-dimensional polymeric networks and linear polymer families with variable lateral chain lengths. By using our experimental data and others collected in the literature in order to scan a large domain of fragility values, we show that the fragility index m, characterising the glass-forming liquid, can be correlated to z(T_g) which characterises the glass formed.     

A thermodynamic approach to the selectivity of liquid crystalline reentrant phases

The thermodynamic characteristics and selectivity of sorption of disubstituted benzene, pyridine, and naphthalene by the p-n-nonyloxybenzoyloxy-p′-cyanoazobenzene, p-n-hexyloxycinnamoyloxy-p′-cyanoazobenzene liquid crystalline phases and their mixture was studied by gas chromatography. The reentrant nematic phase of a mixture of mesogens was found to possess high selectivity to structural isomers. The results of manifestation of liquid crystalline phase selectivity are discussed on the basis of the enthalpy and entropy characteristics of solution of sorbates.     

Thermodynamic basis for cluster kinetics: Prediction of the fragility of marginal metallic glass-forming liquids

Due to the inaccessibility of the supercooled region of marginal metallic glasses (MMGs) within the experimental time window, we study the cluster kinetics above the liquidus temperature, Tl, to acquire information on the fragility of the MMG systems. The thermodynamic basis for the stability of locally ordered structure in the MMG liquids is discussed in terms of the two-order-parameter model. It is found that the Arrhenius activation energy of clusters, Deltah, is proportional to the chemical mixing enthalpy of alloys, DeltaH(chem). Fragility of the MMG forming liquids can be described by the ratio of the absolute DeltaH(chem) value to the glass transition temperature, Tg. The manner of vitrification during rapid solidification is an important factor for the discrepancy between the data presented in this paper and the prediction of the two-order-parameter model concerning the relation between Delta h and the liquid fragility.     

Correlation between thermodynamic and kinetic fragilities in nonpolymeric glass-forming liquids

A phenomenological relationship between reduced excess heat capacity of supercooled liquid DeltaC(p)(exc)(T(g))DeltaS(m) at the glass transition temperature T(g), fragility index m, and reduced glass transition temperature T(rg)=T(g)T(m), where T(m) is the melting (liquidus) temperature, was derived for fragile nonpolymeric glass-forming liquids under the assumptions that the fragile behavior of these liquids is described by the Vogel-Fulcher-Tammann (VFT) equation; the excess heat capacity of liquid is inversely proportional to the absolute temperature and the VFT temperature T(0) is equal to the Kauzmann temperature T(K). It was found that DeltaC(p)(exc)(T(g))DeltaS(m) is a composite function of m and T(rg), which indicates that the empirical correlation DeltaC(p)(exc)(T(g))DeltaS(m)=0.025m recently identified by Wang et al. [J. Chem Phys. 125, 074505 (2006)] is probably valid only for liquids which have nearly the same values of T(rg).     

A combinatorial approach to branched polymers’ statistics

At least ideally, a certain class of polymers presents itself as a collection (set) of connected components. Each of these components is a cycle of trees, that is branched polymers eventually rooted on a cycle. We derive (and study) an equilibrium statistical model that accounts for the main connectivity features of such structures, whose origin is to be found in combinatorial probability. Phase transition (gel–soltransition) is shown to occur when some internal control parameter crosses one (critical parameter). Various structural asymptotic results are shown to be available using singularity analysis. This revised version was published online in July 2006 with corrections to the Cover Date.     

The short time regime of segmental dynamics of glass-forming polymers

The short time regime (10⁻¹³ s ≤ t ≤ 10⁻¹¹ s) of the segmental dynamics of several glass-forming polymers with different chemical microstructure and glass-transition temperature has been investigated by means of time of flight (TOF) neutron scattering techniques. In this paper we present a summary of the main results obtained as well as the theoretical framework proposed by us to interpret these results. The main conclusion is that the segmental dynamics of glass-forming polymers display in the very short time range (t = 2 ps) a crossover from a simple exponential behaviour towards a non-exponential regime. The first exponential decay, which is controlled by C-C rotational barriers, can be understood as a trace of the behaviour of the system in absence of the effects (correlations, cooperativity, memory effects…) which characterise the dense supercooled liquid like state against the normal liquid state. The non-exponential regime at t > 2 ps corresponds to what is usually understood as α and β relaxations. Some implications of these results are also discussed.     

A thermodynamic approach to the anchoring phenomenon in the nematic liquid crystal-substrate system

The phenomenon of anchoring in the nematic liquid crystal-amorphous substrate system is considered and model independent definitions of the surface nematic director, the surface tension and the anchoring energy coefficient are proposed. Then the Landau-de Gennes model of the system is studied for a specific choice of the surface parameters, which leads to a continuous homeotropic-conical anchoring transition. The free energy as a function of the director at a distance l from the surface is found. It is shown that its form is different in two regions of the temperature-distance plane separated by the line of a Freedericksz transition. The asymptotic behaviour of the free energy for large l and for infinitesimal deviations of the director from the anchoring direction is studied. It is found that the asymptotic formula holds also in the vicinity of the anchoring transition. Finally, the results of numerical studies of the Landau-de Gennes model are compared with the predictions of a simple phenomenological model.     

A molecular approach to chain entanglement in linear polymers

The phenomenon of chain entanglement in undiluted linear amorphous polymers is treated by calculating the probability of forming closed intramolecular loops. Adoption of the rotational isomeric state model of polymer chains permits an appropriate accounting of the detailed molecular structure to be made through the configurational characteristics of the polymer. The second (〈r〉₀) and fourth (〈r〉₀) moments of the vector r_hk connecting groups h and k in the isolated polymer chain and averaged over all chain conformations are calculated and used to evaluate the probability W_x(0) that r_hk is 0, or that an intramolecular loop of x = k ? h bonds is formed. Several linear polymers with widely differing molecular structures are treated. An attempt is made to correlate the degree of chain entanglement they manifest in the bulk with their ability to fold back upon themselves to form closed intramolecular loops.     

Liquid–liquid transition in polymers and glass-forming liquids

It is shown that many simple glass-forming liquids exhibit a phenomenon known in the area of polymer science as the liquid–liquid transition. The phenomenon manifests itself as a third-order transition in the equilibrium liquid-specific heat data around approximately 1.2 T_g and also as a bifurcation of the liquid relaxation into primary and secondry processes. It is stressed that the above phenomenon is due to a smooth changeover of the liquid from one dynamic regime to the other and hence is not due to any real phase transition. It is suggested that a liquid cluster kind of picture for the supercooled liquid regime, is capable of explaining the above phenomenon and is consistent with observation made on polymers and monomeric liquids. © 1993 John Wiley & Sons, Inc.     

New approach to filled polymers

Mechanopolymerization of pentabromobenzyl (mono)acrylate (PBB-MA) on the surface of inorganic fillers Mg(OH)₂ and CaCO₃ was studied. The role of activated surface of fillers was investigated using DSC and FTIR. The influence of milling time and of the filler chemical content on polymerization starting temperature and polymerization enthalpy was studied using DSC. It was shown that an increase of the filler concentration leads to a higher maximum conversion degree. The correlation between conversion kinetics and polymerization enthalpy of the material notpolymerized during milling was shown. This paper was presented on the Second Conference of The Israel Group of Mechanochemistry.     

Dimethylsubstituted pyrroles: A new approach to protective polymers

The development of sacrificial or protective films based on dimethylpyrrole analogues is described. The design considerations required for successful electropolymerisation of the monomer and the subsequent, selective dissolution of the film is described. A general synthetic strategy is presented for the formation of a diverse range of bifunctional monomers which, when polymerised, can be subsequently removed after exposure to hydroxylamine under neutral aqueous conditions at room temperature. Film formation and removal has been studied using cyclic voltammetry and electrochemical quartz crystal microbalance (EQCM) studies.