Residual Configurational Entropy Research Articles

Generalized entropy theory of glass-formation in fully flexible polymer melts

The generalized entropy theory (GET) offers many insights into how molecular parameters influence polymer glass-formation. Given the fact that chain rigidity often plays a critical role in understanding the glass-formation of polymer materials, the GET was originally developed based on models of semiflexible chains. Consequently, all previous calculations within the GET considered polymers with some degree of chain rigidity. Motivated by unexpected results from computer simulations of fully flexible polymer melts concerning the dependence of thermodynamic and dynamic properties on the cohesive interaction strength (ϵ), the present paper employs the GET to explore the influence of ϵ on glass-formation in models of polymer melts with a vanishing bending rigidity, i.e., fully flexible polymer melts. In accord with simulations, the GET for fully flexible polymer melts predicts that basic dimensionless thermodynamic properties (such as the reduced thermal expansion coefficient and isothermal compressibility) are universal functions of the temperature scaled by ϵ in the regime of low pressures. Similar scaling behavior is also found for the configurational entropy density in the GET for fully flexible polymer melts. Moreover, we find that the characteristic temperatures of glass-formation increase linearly with ϵ and that the fragility is independent of ϵ in fully flexible polymer melts, predictions that are again consistent with simulations of glass-forming polymer melts composed of fully flexible chains. Beyond an explanation of these general trends observed in simulations, the GET for fully flexible polymer melts predicts the presence of a positive residual configurational entropy at low temperatures, indicating a return to Arrhenius relaxation in the low temperature glassy state.

Frustration and Self-Ordering of Topological Defects in Ferroelectrics.

A first-principles-based effective Hamiltonian technique is used to investigate the interplay between geometrical frustration and the ordering of topological defects in a ferroelectric nanocomposite consisting of a square array of BaTiO_{3} nanowires embedded in a Ba_{0.15}Sr_{0.85}TiO_{3} matrix. Different arrangements of the wires' chiralities geometrically frustrate the matrix, which in response exhibits point topological defects featuring self-assembled ordered structures spatially fluctuating down to the lowest temperatures. These fluctuations thereby endow the system with residual configurational entropy from which many properties characteristic of geometric frustration, such as the ground state degeneracy and the broadness of the dielectric response, are further found to originate.

Exothermic relaxation and endothermic recrystallization of amorphous zirconium tungstate

In a previous work, we have shown, by means of x-ray diffraction and differential thermal analysis measurements, that amorphous zirconium tungstate (a-ZrW${}_{2}$O${}_{8}$) undergoes endothermic recrystallization upon heating to above 900 K. Later on, the anomalous endothermic recrystallization did not become evident in results from drop calorimetry experiments conducted with zirconium tungstate. In this work, we provide evidences in support of the endothermic recrystallization of this compound and show that an exothermic structural relaxation prior to recrystallization may be the cause of the apparent controversy on the nature of the a-ZrW${}_{2}$O${}_{8}$ recrystallization. The net enthalpy of recrystallization was estimated as $+1.8$ kJ/mol. We also demonstrate, by means of in situ synchrotron x-ray diffraction measurements at high temperature, that a-ZrW${}_{2}$O${}_{8}$ recrystallizes into $\ensuremath{\beta}$-ZrW${}_{2}$O${}_{8}$ which, upon cooling, converts to $\ensuremath{\alpha}$-ZrW${}_{2}$O${}_{8}$. The residual configurational entropy of (nonrelaxed) a-ZrW${}_{2}$O${}_{8}$ at 0 K was estimated as 8 Jgat${}^{\ensuremath{-}1}$K${}^{\ensuremath{-}1}$.

The residual configurational entropy below the glass transition: Determination for two commercial optical glasses

Abstract Essentially from differential scanning calorimetry and viscosimetry, the residual configurational entropy below the glass transition is determined for two linearly cooled commercial optical glasses, K7™ and N-LaK12™ from SCHOTT. The procedure is according to the conventional understanding of glass entropy and the conventional description of the configurational state by a distribution of fictive temperatures. For a cooling rate of 10 K/min, the residual entropy values found below the glass transition are 0.146 J/(g K) for K7™ and 0.148 J/(g K) for N-LaK12™. The result is discussed comparing with both the lower limit for the residual entropy resulting from the reversibly exchanged heat ( ∫ dq / T , ‘Clausius limit’) and the upper limit given by the configurational entropy of an equilibrium liquid with the same fictive temperature. The difference between the residual entropy and its lower limit is equal to the entropy generation due to the fall-out from equilibrium during linear cooling. The difference between the residual entropy and its upper limit is the driving force of the crossover- (or Kovacs-) effect. It turns out that the difference between the residual entropy and the Clausius limit is very small. The values found amount to less than 0.0001 J/(g K) for both glasses. Therefore, this difference can be neglected concerning the extrapolation of the Adam–Gibbs relation to low temperatures.

Methyl Dynamics in Proteins from NMR Slowly Relaxing Local Structure Spin Relaxation Analysis: A New Perspective

NMR spin relaxation of (2)H nuclei in (13)CH(2)D groups is a powerful method for studying side-chain motion in proteins. The analysis is typically carried out with the original model-free (MF) approach adapted to methyl dynamics. The latter is described in terms of axial local motions around, and of, the methyl averaging axis, mutually decoupled and independent of the global motion of the protein. Methyl motion is characterized primarily by the axial squared order parameter, S(axis)2, associated with fluctuations of the methyl averaging axis. This view is shown to be oversimplified by applying to typical experimental data the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Adv. Chem. Phys. 1993, 83, 89) which can be considered the generalization of the MF approach. Neglecting mode coupling and the asymmetry of the local ordering and treating approximately features of local geometry imply inaccurate values of S(axis)2, hence of the residual configurational entropy derived from it. S(axis)2, interpreted as amplitude of motion, was found to range from near disorder to almost complete order. Contrary to this picture, we find with the SRLS approach a moderate distribution in the magnitude of asymmetric local ordering and significant variation in its symmetry. The latter important property can be associated implicitly with the contribution of side-chain rotamer jumps. This is consistent with experimental residual dipolar coupling studies and theoretical work based on molecular dynamics simulations and molecular mechanics considerations. Configurational entropy is obtained in the SRLS approach directly from experimentally determined asymmetric potentials. Inconsistency between order parameters from 2H relaxation and from eta(HC-HH) cross-correlation and increase in order parameters with increasing temperature were observed with the MF approach. These discrepancies are reconciled, and physically tenable temperature dependence is obtained with the SRLS approach.

Topological derivation of shape exponents for stretched exponential relaxation

In homogeneous (ideal) glasses, the important dimensionless stretched-exponential shape parameter beta is described by magic (not adjusted) simple fractions derived from fractal configuration spaces of effective dimension d* determined by different topological axioms (rules) in the presence (absence) of a forcing electric field. The rules are based on a new central principle for defining glassy states: equal a priori distributions of fractal residual configurational entropy. Our approach and its beta estimates are fully supported by the results of relaxation measurements involving many different glassy materials and probe methods. The present unique topological predictions for beta typically agree with observed values to approximately 1% and indicate that for field-forced conditions beta should be constant for appreciable ranges of such exogenous variables as temperature and ionic concentration, as indeed observed using appropriate frequency-domain data analysis. The present approach can also be inverted and used to test sample homogeneity and quality.

Configurational entropy of native proteins

Simulations of the residual configurational entropy of a protein in the native state suggest that it is nearly an order of magnitude larger than the entropy of denaturation. The implications of this result are discussed.

Alloying effect on the viscous flow in metallic glasses

The temperature dependence of viscosities near the glass transition is measured from the rates of thermal transformation for metallic glasses PtNiP, PdNiP, NiPBA1 and (Fe, Co)PBA1. Alloying among metallic elements which lowers the glass transition temperature T g lowers the ideal glass transition temperature T 0, but raises the residual configurational entropy S g and the activation energies for “diffusive” rearrangement, Δμ ∗ , of the alloying glasses, while compositional ordering associated with the addition of metalloids raises the T g and T 0 and lowers the S g and Δμ ∗ . Results are correlated to the atomic ordering and stability of the glasses. The extracted free volume and the critical diffusive volume are much smaller, by a factor of 4, for metallic glasses than for many other glasses.