Jalim Singh and Prasanth P Jose Published 5 November 2020 • © 2020 IOP Publishing Ltd
Journal of Physics: Condensed Matter, Volume 33, Number 5
Molecular dynamics simulations are performed on a system of model linear polymers to look at the violations of Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations near the mode coupling theory transition temperature Tc at three (one higher and two lower) densities. At low temperatures, both lower density systems show stable gas-supercooled-liquid coexistence whereas the higher density system is homogeneous. We show that monomer density relaxation exhibits SE violation for all three densities, whereas molecular density relaxation shows a weak violation of the SE relation near Tc in both lower density systems. This study identifies disparity in monomer mobility and observation of jumplike motion in the typical monomer trajectories resulting in the SE violations. In addition to the SE violation, a weak SED violation is observed in the gas-supercooled-liquid coexisting domains of the lower densities. Both lower density systems also show a decoupling of translational and rotational dynamics in this polymer system.
Nature Communications 3, Article number: 1161 (2012) doi:10.1038/ncomms2177
Grains and glasses, widely different materials, arrest their motions upon decreasing temperature and external load, respectively, in common ways, leading to a universal jamming phase diagram conjecture. However, unified theories are lacking, mainly because of the disparate nature of the particle interactions. Here we demonstrate that folded proteins exhibit signatures common to both glassiness and jamming by using temperature- and force-unfolding molecular dynamics simulations. Upon folding, proteins develop a peak in the interatomic force distributions that falls on a universal curve with experimentally measured forces on jammed grains and droplets. Dynamical signatures are found as a dramatic slowdown of stress relaxation upon folding. Together with granular similarities, folding is tied not just to the jamming transition, but a more nuanced picture of anisotropy, preparation protocol and internal interactions emerges. Results have implications for designing stable polymers and can open avenues to link protein folding to jamming theory.
Prasanth P. Jose and Grzegorz Szamel
Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523, USA
We use Brownian dynamics computer simulations to investigate single-chain dynamics in a semidilute polymer solution undergoing a steady, uniform shear flow. In the presence of the shear flow, the system used in the present study exhibits anisotropic structure factors, often referred to as butterfly patterns, which rotate with increasing shear rate [P. P. Jose and G. Szamel, J. Chem. Phys. 127,114905 (2007)]. The rotation of these patterns correlates with shear thinning of the solution. In order to elucidate the microscopic origin of this behavior, we have investigated the change in the single-chain dynamics in the solution: We have focused on the relaxation of the end-to-end vector, the Rouse modes, and the radius of gyration tensor. In equilibrium and for small shear rates, these quantities show double exponential relaxation. With increasing shear rate, they show oscillatory relaxation, which hints at the tumbling motion of the chain. In the high shear rate regime, the frequency of the oscillations of the end-to-end vector autocorrelation function shows a power law dependence on the shear rate. We have compared the single-chain dynamics in the semidilute solution with that in a dilute solution. An analysis of the instantaneous values of the radius of gyration tensor, the end-to-end distance, and the normal stress along the system's trajectory reveals a synchronization of the fluctuations of these quantities.
Prasanth P. Jose and Grzegorz Szamel
Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523 USA
We use Brownian dynamics computer simulations to investigate the structure of a semidilute polymer solution undergoing a steady, uniform shear flow. We find that the contributions to structure factor from intra- and interchain correlations, which cancel each other almost completely for an equilibrium semidilute solution, are modified in different ways by the shear flow. Incomplete cancellation of these contributions leads to anisotropic patterns that resemble those observed in light scattering experiments on sheared semidilute solutions [Wu et al., Phys. Rev. Lett. 66, 2408 (1991)]. For small wave vectors the structure factor change is dominated by the interchain contribution. We also monitor the distortion of the pair correlation function and show that for small distances it is dominated by the intrachain contribution. Finally, we investigate nonlinear shear viscosity and find that, like the short-distance part of the distortion of the pair correlation function, it is predominantly of intrachain origin
Department of Chemistry, Colorado State University, Fort Collins, Colorado 80523
Biman Bagchi
Solid State and Structural chemistry Unit, Indian Institute of Science, Bangalore 560012, India
Relaxation in the nematic liquid crystalline phase is known to be sensitive to its proximity to both isotropic and smectic phases. Recent transient optical Kerr effect (OKE) studies have revealed, rather surprisingly, two temporal power laws at short to intermediate timesand also an apparent absence of the expected exponential decay at longer times. In order to understand this unusual dynamics, we have carried out extensive molecular dynamics simulations of transient OKE and related orientational time correlation functions in a system of prolate ellipsoids (with aspect ratio equal to 3). The simulations find two distinct power laws, with a crossover region, in the decay of the orientational time correlation function at short to intermediate times (in the range of a few picoseconds to a few nanoseconds). In addition, the simulation results fail to recover any long time exponential decay component. The system size dependence of the exponents suggests that the first power law may originate from the local orientational density fluctuations (like in a glassy liquid). The origin of the second power law is less clear and may be related to the long range fluctuations (such as smecticlike density fluctuations)—these fluctuations are expected to involve small free energy barriers. In support of the latter, the evidence of pronounced coupling between orientational and spatial densities at intermediate wave numbers is presented. This coupling is usually small in normal isotropic liquids, but it is large in the present case. In addition to slow collective orientational relaxation, the single particle orientational relaxation is also found to exhibit slow dynamics in the nematic phase in the long time.
Complete breakdown of the Debye model of rotational relaxation near the isotropic-nematic phase boundary: Effects of intermolecular correlations in orientational dynamics
Prasanth P. Jose, Dwaipayan Chakrabarti, and Biman Bagchi
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, Karnataka, India
URL: http://link.aps.org/abstract/PRE/v73/e031705
doi:10.1103/PhysRevE.73.031705
PACS: 61.30.-v, 66.10.Cb
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The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the orientational correlation times
The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the orientational correlation times τl vary as [l(l+1)]−1, where l is the rank of the orientational time correlation function (given in terms of the Legendre polynomial of rank l). One often finds significant deviation from this prediction, in either direction. In supercooled molecular liquids where the ratio τ1∕τ2 falls considerably below 3 (the Debye limit), one usually invokes a jump diffusion model to explain the approach of the ratio τ1∕τ2 to unity. Here we show in a computer simulation study of a standard model system for thermotropic liquid crystals that this ratio becomes much less than unity as the isotropic-nematic phase boundary is approached from the isotropic side. Simultaneously, the ratio τ2∕η, η being the shear viscosity of the liquid, becomes much larger than the hydrodynamic value near the I−N transition. We also analyze the breakdown of the Debye model of rotational diffusion in ratios of higher order orientational correlation times. We show that the breakdown of the DSE model is due to the growth of orientational pair correlation and provide a mode coupling theory analysis to explain the results.
Universal Power Law in the Orientational Relaxation in Thermotropic Liquid Crystals
Dwaipayan Chakrabarti, Prasanth P. Jose, Suman Chakrabarty, and Biman Bagchi
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
URL: http://link.aps.org/abstract/PRL/v95/e197801
doi:10.1103/PhysRevLett.95.197801
PACS: 61.20.Lc, 64.70.Md, 64.70.Pf
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We observe a surprisingly general power law decay at short to intermediate times in orientational relaxation in a variety of modelsystems (both calamitic and discotic, and also lattice) for thermotropic liquid crystals. As all these systems transit across the isotropic-nematic phase boundary, two power law relaxation regimes, separated by a plateau, emerge, giving rise to a steplike feature (well known in glassy liquids) in the single-particle second-rank orientational time correlation function. In contrast to its probable dynamical origin in supercooled liquids, we show that the power law here can originate from the thermodynamic fluctuations of the orientational order parameter, driven by the rapid growth in the second-rank orientational correlation length.
Anomalous glassy relaxation near the isotropic-nematic phase transition
Prasanth P. Jose, Dwaipayan Chakrabarti, and Biman Bagchi
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
URL: http://link.aps.org/abstract/PRE/v71/e030701
doi:10.1103/PhysRevE.71.030701
PACS: 64.70.Md, 64.70.Pf
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Dynamical heterogeneity in a system of Gay-Berne ellipsoids near its isotropic-nematic (I-N) transition, and also in an equimolar mixture of Lennard-Jones spheres and Gay-Berne ellipsoids in deeply supercooled regime, is probed by the time evolution of non-Gaussian parameters (NGP). The appearance of a dominant second peak in the rotational NGP near the I-N transition signals the growth of pseudonematic domains. Surprisingly, such a second peak is instead observed in the translational NGP for the glassy binary mixture. Localization of orientational motion near the I-N transition is found to be responsible for the observed anomalous orientational relaxation.
Prasanth P. Jose and Biman Bagchi
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012, India
Recent optical Kerr effect experiments have shown that orientational relaxation of nematogens shows a pronounced slow down of the response function at intermediate times and also a power law decay near the isotropic-nematic (I-N) transition. In many aspects, this behavior appears to be rather similar to the ones observed in the supercooled liquid near-glass transition [Cang et al., J. Chem. Phys. 118, 9303 (2003)]. We have performed molecular dynamics simulations of model nematogens (Gay-Berne with aspect ratio 3) to explore the viscoelasticity near the I-N transition and also investigated the correlation of viscoelasticity (if any) with orientational relaxation. It is found that although the viscosity indeed undergoes a somewhat sharper than normal change near the I-N transition, it is not characterized by any divergencelike behavior (like the ones observed in the supercooled liquid). The rotational friction, on the other hand, shows a much sharper rise as the I-N transition is approached. Interestingly, the probability distribution of the amplitude of the three components of the stress tensor shows anisotropy near the I-N transition—similar anisotropy has also been seen in the deeply supercooled liquid [Phys. Rev. Lett. 89, 25504 (2002)]. Frequency dependence of viscosity shows several unusual behaviors: (a) There is a weak, power law dependence on frequency [η′(ω)∼ω−α] at low frequencies and (b) there is a rapid increase in the sharp peak observed in η′(ω) in the intermediate frequency on approach to the I-N transition density. These features can be explained from the stress-stress time correlation function. The angular velocity correlation function also exhibits a power law decay in time. The reason for this is discussed.
Prasanth P. Jose and Biman Bagchi
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560012, India
Recent Kerr relaxation experiments by Gottke et al. [J. Chem. Phys. 116, 360 (2002); 116, 6339 (2002)] have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic–nematic phase transition (INPT) of nematogens of rather small aspect ratio, κ (κ≃3–4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay–Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t−α) with exponent α∼2/3.
More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau–de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.
Prasanth P. Jose and Biman Bagchi
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012, India
A new master equation to mimic the dynamics of a collection of interacting random walkers in an open system is proposed and solved numerically. In this model, the random walkers interact through excluded volume interaction (single-file system); and the total number of walkers in the lattice can fluctuate because of exchange with a bath. In addition, the movement of the random walkers is biased by an external perturbation. Two models for the latter are considered: (1) an inverse potential (V∝1/r), where r is the distance between the center of the perturbation and the random walker and (2) an inverse of sixth power potential (V∝1/r6). The calculated density of the walkers and the total energy show interesting dynamics. When the size of the system is comparable to the range of the perturbing field, the energy relaxation is found to be highly nonexponential. In this range, the system can show stretched exponential (e−(t/τs)β)
and even logarithmic time dependence of energy relaxation over a limited range of time. Introduction of density exchange in the lattice markedly weakens this nonexponentiality of the relaxation function, irrespective of the nature of perturbation.
Prasanth P. Jose and Biman Bagchi
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-12, India
When radiation is scattered by a medium, a part of its momentum is transferred to the target particles. This is purely a mechanical force which comes into effect when radiation is not coherently interacting. This force is known in literature as radiation pressure. Recent experimental studies have demonstrated the feasibility of using radiation pressure of a laser beam as a tool for cluster formation in solution. In this paper we describe the Brownian dynamics simulation of solute molecules under the perturbation induced by laser radiation. Here the force field generated by a laser beam in the fundamental mode is modeled as that of a two-dimensional harmonic oscillator. The radial distribution function of the perturbed system gives indication of high inhomogeneities in the solute distribution. An explicit analysis of the nature of these clusters is carried out by calculating the density–density correlation functions in the plane perpendicular to beam direction g(rxy); and along the direction of beam g(z), they give an average picture of shell structure formation in the different directions. The relaxation time of the first shell structure calculated from the van Hove correlation function is found to be relatively large in the perturbed solution. This is the signature of formation of stable nanoclusters in the presence of the radiation field. Our study on the dynamics of solute molecules during the cluster formation and dissolution gives the duration of collective relaxation, far away from the equilibrium to an equilibrium distribution. This relaxation time is found to be large for a perturbed solution.