arXiv subjects

C. M. Roland

Publications and source records attributed to C. M. Roland.

At least 37 records · Page 2Linked to original sources

arXiv2012

Limits to Poisson's ratio in isotropic materials - general result for arbitrary deformation

The lower bound usually cited for Poisson's ratio ν is -1, derived from the relationship between ν and the bulk and shear moduli. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on ν for isotropic materials is actually 1/5, a value also consistent with experimental measurements on real materials. Herein we generalize this result, first by analyzing expressions for ν in terms of six common elastic constants, and then by considering arbitrary strains. The results corroborate the prior finding that 1/5 <= ν for linear elasticity to be applicable.

cond-mat.mtrl-sci↗

arXiv2012

Molecular dynamics simulations of the Johari-Goldstein relaxation in a molecular liquid

Molecular dynamics simulations (mds) were carried out to investigate the reorientational motion of a rigid (fixed bond length), asymmetric diatomic molecule in the liquid and glassy states. In the latter the molecule reorients via large-angle jumps, which we identify with the Johari-Goldstein (JG) dynamics. This relaxation process has a broad distribution of relaxation times, and at least deeply in the glass state, the mobility of a given molecule remains fixed over time; that is, there is no dynamic exchange among molecules. Interestingly, the JG relaxation time for a molecule does not depend on the local density, although the non-ergodicity factor is weakly correlated with the packing efficiency of neighboring molecules. In the liquid state the frequency of the JG process increases significantly, eventually subsuming the slower alpha-relaxation. This evolution of the JG-motion into structural relaxation underlies the correlation of many properties of the JG- and alpha-dynamics.

cond-mat.soft↗

arXiv2011

Comparing dynamic correlation lengths from an approximation to the four-point dynamic susceptibility and from the picosecond vibrational dynamics

Recently a new approach to the determination of dynamic correlation lengths, ξ, for supercooled liquids, based on the properties of the slow (picosecond) vibrational dynamics, was carried out [L. Hong, V.N. Novikov, and A.P. Sokolov, Phys. Rev. E 83, 061508 (2011)]. Although these vibrational measurements are typically conducted well below the glass transition temperature, Tg, the assumption is that the structure of the liquid is frozen at Tg, so that the ξ characterize dynamic heterogeneity in the supercooled liquid state. We compare ξ from this method to values calculated using an approximation to the four-point dynamic susceptibility. For 26 different materials we find good correlation between the two measures; moreover, the pressure dependences are consistent within the large experimental error. However, ξ from Boson peak measurements above Tg have a different, and unrealistic, temperature dependence.

cond-mat.soft↗

arXiv2011

Networks

The two approaches to analyzing the large strain behavior of rubbery networks are phenomenologically, using strain energy functions drawn from continuum mechanics, and molecular models, which apply statistical mechanics to compute the effect of chain orientation on the entropy. The early rubber elasticity models ignored intermolecular interactions, whereas later developments ("constraint models") included the effect of entanglements or steric constraints on the mechanical stress. These constitutive equations for rubber elasticity are compared to experimental results, and the connection of network elasticity to the relaxation behaviour is discussed. For conventional elastomers there is a compromise between stiffness and strength. Different methods to circumvent this limitation are described. Examples are given of the properties obtained with novel network architectures, including interpenetrating networks, double networks, bimodal networks, miscible heterogeneous networks, and deswollen networks.

cond-mat.soft↗

arXiv2011

Constitutive modeling, non-linear behavior, and the stress-optic law

Constitutive modelling of the stress-strain response of rubbery polymers is described, with an emphasis on the limits to linearity for both neat and filled rubber (the latter due to the Payne effect). Deviations from the Boltzmann superposition principle (time-strain invariance) under reversing strain histories are reviewed, including a discussion of the Mullins effect. The chapter also reviews the application of the stress optic law and the conditions causing its breakdown: internal stress, the glass transition, orientational coupling, and creep recovery. Different empirical rules for nonlinear flow are considered, including the Cox-Merz rule and the relations of Laun and Gleissle.

cond-mat.soft↗

arXiv2011

Connection between dynamics and thermodynamics of liquids on the melting line

The dynamics of a large number of liquids and polymers exhibit scaling properties characteristic of a simple repulsive inverse power law (IPL) potential, most notably the superpositioning of relaxation data as a function of the variable TVγ, where T is temperature, V the specific volume, and γ a material constant. A related scaling law, TmVmΓ, with the same exponent Γ=γ, links the melting temperature Tm and volume Vm of the model IPL liquid; liquid dynamics is then invariant at the melting point. Motivated by a similar invariance of dynamics experimentally observed at transitions of liquid crystals, we determine dynamic and melting point scaling exponents γ and Γ for a large number of non-associating liquids. Rigid, spherical molecules containing no polar bonds have Γ=γ; consequently, the reduced relaxation time, viscosity and diffusion coefficient are each constant along the melting line. For other liquids γ>Γ always; i.e., the dynamics is more sensitive to volume than is the melting point, and for these liquids the dynamics at the melting point slows down with increasing Tm (that is, increasing pressure).

cond-mat.soft↗

arXiv2009

Density scaling in viscous liquids: From relaxation times to four-point susceptibilities

We present numerical calculations of a four-point dynamic susceptibility, chi_4(t), for the Kob-Andersen Lennard-Jones mixture as a function of temperature T and density rho. Over a relevant range of T and rho, the full t-dependence of chi_4(t) and thus the maximum in chi_4(t), which is proportional to the dynamic correlation volume, are invariant for state points for which the scaling variable rho^gamma/T is constant. The value of the material constant gamma is the same as that which superposes the relaxation time, tau, of the system versus rho^gamma/T. Thus, the dynamic correlation volume is directly related to tau for any thermodynamic condition in the regime where density scaling holds. Finally, we examine the conditions under which the density scaling properties are related to the existence of strong correlations between pressure and energy fluctuations.

cond-mat.stat-mech↗

arXiv2009

Density Scaling and Dynamic Correlations in Viscous Liquids

We use a recently proposed method [Berthier L.; Biroli G.; Bouchaud J.P.; Cipelletti L.; El Masri D.; L'Hote D.; Ladieu F.; Pierno M. Science 2005, 310, 1797.] to obtain an approximation to the 4-point dynamic correlation function from derivatives of the linear dielectric response function. For four liquids over a range of pressures, we find that the number of dynamically correlated molecules, Nc, depends only on the magnitude of the relaxation time, independently of temperature and pressure. This result is consistent with the invariance of the shape of the relaxation dispersion at constant relaxation time and the density scaling property of the relaxation times, and implies that Nc also conforms to the same scaling behavior. For propylene carbonate and salol Nc becomes constant with approach to the Arrhenius regime, consistent with the value of unity expected for intermolecularly non-cooperative relaxation.

cond-mat.soft↗

arXiv2009

Pressure-energy correlations and thermodynamic scaling in viscous Lennard-Jones liquids

We use molecular dynamics simulation results on viscous binary Lennard-Jones mixtures to examine the correlation between the potential energy and the virial. In accord with a recent proposal [U. R. Pedersen et. al. Phys. Rev. Lett. 100, 015701 (2008)], the fluctuations in the two quantities are found to be strongly correlated, exhibiting a proportionality constant, Gamma, numerically equal to one-third the slope of an inverse power law approximation to the intermolecular potential function. The correlation is stronger at higher densities, where interatomic separations are in the range where the inverse power law approximation is more accurate. These same liquids conform to thermodynamic scaling of their dynamics, with the scaling exponent equal to Gamma. Thus, the properties of strong correlation between energy and pressure and thermodynamic scaling both reflect the ability of an inverse power law representation of the potential to capture interesting features of the dynamics of dense, highly viscous liquids.

cond-mat.stat-mech↗

arXiv2008

Anomalous properties of the local dynamics in polymer glasses

The emergence of nanoscience has increased the importance of experiments able to probe the very local structure of materials, especially for disordered and heterogeneous systems. This is technologically important; for example, the nanoscale structure of glassy polymers has a direct correlation with their macroscopic physical properties. We have discovered how a local, high frequency dynamic process can be used to monitor and even predict macroscopic behavior in glassy polymers. Polyvinylethylenes vitrified by different chemical and thermodynamic pathways exhibit different densities in the glassy state. We find that the rate and amplitude of a high frequency relaxation mode (the Johari-Goldstein process involving local motion of segments of the chain backbone) can either correlate or anti-correlate with the density. This implies that neither the unoccupied (free) volume nor the configurational entropy governs the local dynamics in any general sense. Rather it is the magnitude of the fluctuations in local density that underlie these nm-scale motions. We show how properties of the dynamics and the density fluctuations can both be interpreted in terms of an asymmetric double well potential. Finally, since fluctuations underlie the macroscopic properties, we argue that information about the latter should be obtainable from characterization of the local dynamics.

cond-mat.soft↗

arXiv2007

Thermodynamic scaling of diffusion in supercooled Lennard-Jones liquids

The manner in which the intermolecular potential u(r) governs structural relaxation in liquids is a long standing problem in condensed matter physics. Herein we show that diffusion coefficients for simulated Lennard-Jones m-6 liquids (8<m<36) in normal and moderately supercooled states are a unique function of the variable rho^g/T, where rho is density and T is temperature. The scaling exponent g is a material specific constant whose magnitude is related to the steepness of the repulsive part of u(r), evaluated around the distance of closest approach between particles probed in the supercooled regime. Approximations of u(r) in terms of inverse power laws are also discussed.

cond-mat.stat-mech↗

arXiv2007

Relationship between non-exponentiality of relaxation and relaxation time at the glass transition

By analyzing the experimental data for various glass-forming liquids and polymers, we find that non-exponentiality $β$ and the relaxation time $τ$ are uniquely related: $\log(τ)$ is an approximately linear function of $1/β$, followed by a crossover to a higher linear slope. We rationalize the observed relationship using a recently developed approach, in which the problem of the glass transition is discussed as the elasticity problem.

cond-mat.dis-nn↗

arXiv2007

An equation for the description of volume and temperature dependences of the dynamics of supercooled liquids and polymer melts

A recently proposed expression to describe the temperature and volume dependences of the structural (or alpha) relaxation time is discussed. This equation satisfies the scaling law for the relaxation times, tau = f(TV^g), where T is temperature, V the specific volume, and g a material-dependent constant. The expression for the function f is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover, providing a description of the dynamics with a minimal number of parameters. The results herein can be reconciled with previously found correlations of the isochoric fragility with both the isobaric fragility at atmospheric pressure and the scaling exponent g.

cond-mat.soft↗

arXiv2007

Effect of entropy on the dynamics of supercooled liquids: New results from high pressure data

We show that for arbitrary thermodynamic conditions, master curves of the entropy are obtained by expressing S(T,V) as a function of TV^g_G, where T is temperature, V specific volume, and g_G the thermodynamic Gruneisen parameter. A similar scaling is known for structural relaxation times,tau = f(TV^g); however, we find g_G < g. We show herein that this inequality reflects contributions to S(T,V) from processes, such as vibrations and secondary relaxations, that do not directly influence the supercooled dynamics. An approximate method is proposed to remove these contributions, S_0, yielding the relationship tau = f(S-S_0).

cond-mat.soft↗

arXiv2006

Thermodynamic interpretation of the scaling of the dynamics of supercooled liquids

The recently discovered scaling law for the relaxation times, tau=f(T,V^g), where T is temperature and V the specific volume, is derived by a revision of the entropy model of the glass transition dynamics originally proposed by Avramov [I. Avramov, J. Non-Cryst. Solids 262, 258 (2000).]. In this modification the entropy is calculated by an alternative route, while retaining the approximation that the heat capacity is constant with T and P. The resulting expression for the variation of the relaxation time with T and V is shown to accurately fit experimental data for several glass-forming liquids and polymers over an extended range encompassing the dynamic crossover. From this analysis, which is valid for any model in which the relaxation time is a function of the entropy. we find that the scaling exponent g can be identified with the Gruneisen constant.

cond-mat.soft↗

arXiv2006

Scaling of the Local Dynamics and the Intermolecular Potential

The experimental fact that relaxation times, tau, of supercooled liquids and polymers are uniquely defined by the quantity TV^g, where T is temperature, V specific volume, and g a material constant, leads to a number of interpretations and predictions concerning the dynamics of vitrification. Herein we examine means to determine the scaling exponent g apart from the usual superpositioning of relaxation data. If the intermolecular potential can be approximated by an inverse power law, as implied by the TV^g scaling, various equations are derived relating g to the Gruneisen parameter and to a common expression for the pressure derivative of the glass temperature. In addition, without assumptions, g can be obtained directly from pressure-volume-temperature data. These methods for determining g from molecular or thermodynamic properties are useful because they enable the P- and V-dependences of tau to be obtained, and thereby various analyses of the dynamics to be explored, without the need to carry out relaxation measurements beyond ambient pressure.

cond-mat.soft↗

arXiv2006

What can we learn by squeezing a liquid

Relaxation times for different temperatures, T, and specific volumes, V, collapse to a master curve versus TV^g, with g a material constant. The isochoric fragility, m_V, is also a material constant, inversely correlated with g. From these we obtain a 3-parameter function, which fits accurately relaxation times of several glass-formers over the supercooled regime, without any divergence below Tg. Although the 3 parameters depend on the material, only g significant varies; thus, by normalizing material-specific quantities related to g, a universal power law for the dynamics is obtained.

cond-mat.soft↗

arXiv2006

Volume Effects on the Glass Transition Dynamics

The role of jamming (steric constraints) and its relationship to the available volume is addressed by examining the effect that certain modifications of a glass-former have on the ratio of its isochoric and isobaric activation enthalpies. This ratio reflects the relative contribution of volume (density) and temperature (thermal energy) to the temperature-dependence of the relaxation times of liquids and polymers. We find that an increase in the available volume confers a stronger volume-dependence to the relaxation dynamics, a result at odds with free volume interpretations of the glass transition.

cond-mat.soft↗