Adam-Gibbs based model to describe the single component dynamics in miscible polymer blends under hydrostatic pressure

We present in this work a new model to describe the component segmental dynamics in miscible polymers blends as a function of pressure, temperature, and composition. The model is based on a combination of the Adam-Gibbs (AG) theory and the concept of the chain connectivity. In this paper we have extended our previous approach [D. Cangialosi et al. J. Chem. Phys. 123, 144908 (2005)] to include the effects of pressure in the component dynamics of miscible polymer blends. The resulting model has been tested on poly(vinyl methyl ether) (PVME)/polystyrene (PS) blends at different concentrations and in the temperature range where the system is in equilibrium. The results show an excellent agreement between the experimental and calculated relaxation times using only one fitting parameter. Once this parameter is known the model allows calculating the size of the relevant length scale where the segmental relaxation of the dielectrically active component takes place, i.e., the so called cooperative rearrangement region (CRR) in the AG framework. Thus the size of the CRR for PVME in the blends with PS has been determined as well as its dependence with pressure, temperature, and concentration.     

Thermorheological complexity of poly(methyl methacrylate)/poly(vinylidene fluoride) miscible polymer blend: Terminal and segmental levels

Oscillatory shear rheometry data for a miscible blend of 20 wt % poly(vinylidene fluoride) (PVDF) in poly(methyl methacrylate) (PMMA) shows breakdown of time–temperature superposition for this blend. A comparison between glass transition temperature which PMMA chains sense in the blend and effective glass transition temperature of this component indicates that, the Lodge–McLeish model can describe terminal dynamics of PMMA. In addition, terminal dynamics of PVDF chains in the blend is similar to that of its pure state in agreement with the mentioned model. At segmental level, dynamic mechanical thermal analysis of four wholly amorphous blends suggests that cooperativity of molecular motions decreases upon addition of 30 and 40 wt % PVDF to PMMA. This behavior has been confirmed via calculation of degree of fragility which presumably is attributed to strong tendency of PVDF chains to self‐association rather than inter‐association with PMMA chains according to the FTIR results. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2860–2870, 2007     

The single chain limit of structural relaxation in a polyolefin blend

The influence of composition on component dynamics and relevant static properties in a miscible polymer blend is investigated using molecular dynamics simulation. Emphasis is placed on dynamics in the single chain dilution limit, as this limit isolates the role of inherent component mobility in the polymer's dynamic behavior when placed in a blend. For our systems, a biased local concentration affecting dynamics must arise primarily from chain connectivity, which is quantified by the self-concentration, because concentration fluctuations are minimized due to restraints on chain lengths arising from simulation considerations. The polyolefins simulated [poly(ethylene-propylene) (PEP) and poly(ethylene-butene) (PEB)] have similar structures and glass transition temperatures, and all interactions are dispersive in nature. We find that the dependence of dynamics upon composition differs between the two materials. Specifically, PEB (slower component) is more influenced by the environment than PEP. This is linked to a smaller self-concentration for PEB than PEP. We examine the accuracy of the Lodge-McLeish model (which is based on chain connectivity acting over the Kuhn segment length) in predicting simulation results for effective concentration. The model predicts the simulation results with high accuracy when the model's single parameter, the self-concentration, is calculated from simulation data. However, when utilizing the theoretical prediction of the self-concentration the model is not quantitatively accurate. The ability of the model to link the simulated self-concentration with biased local compositions at the Kuhn segment length provides strong support for the claim that chain connectivity is the leading cause of distinct mobility in polymer blends. Additionally, the direct link between the willingness of a polymer to be influenced by the environment and the value of the self-concentration emphasizes the importance of the chain connectivity. Furthermore, these findings are evidence that the Kuhn segment length is the relevant length scale controlling segmental dynamics.     

Combining configurational entropy and self-concentration to describe the component dynamics in miscible polymer blends

We provide a new approach to describe the component segmental dynamics of miscible polymer blends combining the concept of chain connectivity, expressed in terms of the self-concentration, and the Adam-Gibbs model. The results show an excellent agreement between the prediction of our approach and the experimental data. The self-concentrations obtained yield length scales between 1 and 3.2 nm depending on the temperature, the flexibility of the polymer, expressed in terms of the Kuhn segment, and its concentration in the blends, at temperatures above the glass transition range of the blend.     

Investigating the effect of nanolayered silicates on blend segmental dynamics and minor component relaxation behavior in poly(ethylene oxide)/poly(methyl methacrylate) miscible blends

Polymer–silicate nanocomposites based on poly (ethylene oxide), PEO, poly(methyl methacrylate), PMMA, and sodium montmorillonite clay were fabricated and characterized to investigate the effect of nanolayered silicates on segmental dynamics of PEO/PMMA blends. X‐ray results indicate the formation of an exfoliated morphology in the nanocomposites. At low silicate contents, an enhancement in segmental dynamics of blend nanocomposites and also PEO, minor component in blend, is observed at temperature region below blend glass transition. This result can be attributed to the improvement of the confinement effect of rigid PMMA matrix on the PEO chains by introducing a low amount of layered silicates. On the other hand, at high silicate contents, an enhancement in segmental dynamics of blend nanocomposites and PEO is observed at temperature region above blend glass transition. This behavior could be interpreted based on the reduction of monomeric friction between two polymer components, which can facilitate segmental motions of blend components in nanocomposite systems. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

A semiclassical hybrid approach to many particle quantum dynamics

We analytically derive a correlated approach for a mixed semiclassical many particle dynamics, treating a fraction of the degrees of freedom by the multitrajectory semiclassical initial value method of Herman and Kluk [Chem. Phys. 91, 27 (1984)] while approximately treating the dynamics of the remaining degrees of freedom with fixed initial phase space variables, analogously to the thawed Gaussian wave packet dynamics of Heller [J. Chem. Phys. 62, 1544 (1975)]. A first application of this hybrid approach to the well studied Secrest-Johnson [J. Chem. Phys. 45, 4556 (1966)] model of atom-diatomic collisions is promising. Results close to the quantum ones for correlation functions as well as scattering probabilities could be gained with considerably reduced numerical effort as compared to the full semiclassical Herman-Kluk approach. Furthermore, the harmonic nature of the different degrees of freedom can be determined a posteriori by comparing results with and without the additional approximation.     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245     

Study of thermal properties of the metastable supersaturated vapor with the integral equation method

Pressure, excess chemical potential, and excess free energy data for different densities of the supersaturated argon vapor at reduced temperatures from 0.7 to 1.2 are obtained by solving the integral equation with perturbation correction to the radial distribution function [F. Lado, Phys. Rev. 135, A1013 (1964)]. For those state points where there is no solution, the integral equation is solved with the interaction between argon atoms modeled by Lennard-Jones potential plus a repulsive potential with one controlling parameter, alpha exp(-rsigma) and in the end, all the thermal properties are mapped back to the alpha=0 case. Our pressure data and the spinodal obtained from the current method are compared with a molecular dynamics simulation study [A. Linhart et al., J. Chem. Phys. 122, 144506 (2005)] of the same system.     

Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries

A numerical method to simulate the dynamics of polymer solutions in confined geometries has been implemented and tested. The method combines a fluctuating lattice-Boltzmann model of the solvent [Ladd, Phys. Rev. Lett. 70, 1339 (1993)] with a point-particle model of the polymer chains. A friction term couples the monomers to the fluid [Ahlrichs and Dunweg, J. Chem. Phys. 111, 8225 (1999)], providing both the hydrodynamic interactions between the monomers and the correlated random forces. The coupled equations for particles and fluid are solved on an inertial time scale, which proves to be surprisingly simple and efficient, avoiding the costly linear algebra associated with Brownian dynamics. Complex confined geometries can be represented by a straightforward mapping of the boundary surfaces onto a regular three-dimensional grid. The hydrodynamic interactions between monomers are shown to compare well with solutions of the Stokes equations down to distances of the order of the grid spacing. Numerical results are presented for the radius of gyration, end-to-end distance, and diffusion coefficient of an isolated polymer chain, ranging from 16 to 1024 monomers in length. The simulations are in excellent agreement with renormalization group calculations for an excluded volume chain. We show that hydrodynamic interactions in large polymers can be systematically coarse-grained to substantially reduce the computational cost of the simulation. Finally, we examine the effects of confinement and flow on the polymer distribution and diffusion constant in a narrow channel. Our results support the qualitative conclusions of recent Brownian dynamics simulations of confined polymers [Jendrejack et al., J. Chem. Phys. 119, 1165 (2003) and Jendrejack et al., J. Chem. Phys. 120, 2513 (2004)].     

A consistent integral equation theory for hard spheres

The standard integral equation approach is used to extract the bridge function and other correlation functions of hard spheres fluid. To achieve this, we first use a recent consistent closure relation proposed by Bomont et al. [J. Chem. Phys. 119, 2188 (2003)] that has already proven to be accurate to describe the Lennard-Jones fluid properties. Second, we take advantage of the coherent scheme derived by Bomont [J. Chem. Phys. 119, 11484 (2003)] to calculate the excess chemical potential, the entropy and some relative transport properties. Very good agreement is obtained for structural quantities and thermodynamic properties as compared to exact data at densities ranging from 0.1 to 0.9.     

A new method of stabilization and characterization of the interface in binary polymer blends by irradiation: A positron annihilation study

New methods for stabilizing the interface of partially miscible and immiscible binary polymer blends and characterizing such an interface are described here. Interfacial modifications in four binary polymer blend systems namely PS/PMMA, PVC/EVA, PP/NBR, and PVC/SAN were induced by e‐beam and microwave irradiation. These changes have been characterized in terms of free volume measured by Positron lifetime technique and DSC as supplementary to free volume data. The changes observed in free volume parameters upon irradiation could not be connected to the changes at the interface and also not specific to composition of the blend. Owing to this limitation, we exploited the usefulness of hydrodynamic interaction parameter α derived from the very same free volume data to monitor the changes at the interface. The present results demonstrated that α is effective in revealing the changes at the interface and can be used to characterize the interfacial properties in partially miscible and immiscible polymer blends. Further, the results clearly show that microwave irradiation is a better route to stabilize the interface of a partially miscible or immiscible blend if its component polymers contain polar groups. E‐beam irradiation seems to be better route if the component polymers of the blend contain no polar groups. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 619–632, 2009     

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.     

Comparison of different methods for calculating the paramagnetic relaxation enhancement of nuclear spins as a function of the magnetic field

The enhancement of the spin-lattice relaxation rate for nuclear spins in a ligand bound to a paramagnetic metal ion [known as the paramagnetic relaxation enhancement (PRE)] arises primarily through the dipole-dipole (DD) interaction between the nuclear spins and the electron spins. In solution, the DD interaction is modulated mostly by reorientation of the nuclear spin-electron spin axis and by electron spin relaxation. Calculations of the PRE are in general complicated, mainly because the electron spin interacts so strongly with the other degrees of freedom that its relaxation cannot be described by second-order perturbation theory or the Redfield theory. Three approaches to resolve this problem exist in the literature: The so-called slow-motion theory, originating from Swedish groups [Benetis et al., Mol. Phys. 48, 329 (1983); Kowalewski et al., Adv. Inorg. Chem. 57, (2005); Larsson et al., J. Chem. Phys. 101, 1116 (1994); T. Nilsson et al., J. Magn. Reson. 154, 269 (2002)] and two different methods based on simulations of the dynamics of electron spin in time domain, developed in Grenoble [Fries and Belorizky, J. Chem. Phys. 126, 204503 (2007); Rast et al., ibid. 115, 7554 (2001)] and Ann Arbor [Abernathy and Sharp, J. Chem. Phys. 106, 9032 (1997); Schaefle and Sharp, ibid. 121, 5387 (2004); Schaefle and Sharp, J. Magn. Reson. 176, 160 (2005)], respectively. In this paper, we report a numerical comparison of the three methods for a large variety of parameter sets, meant to correspond to large and small complexes of gadolinium(III) and of nickel(II). It is found that the agreement between the Swedish and the Grenoble approaches is very good for practically all parameter sets, while the predictions of the Ann Arbor model are similar in a number of the calculations but deviate significantly in others, reflecting in part differences in the treatment of electron spin relaxation. The origins of the discrepancies are discussed briefly.     

Understanding Molecular Dynamics with Stochastic Processes via Real or Virtual Dynamics

Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation[J. Chem. Phys. 147 , 184104 (2017)] in principle exists in other types of stochastic thermostats as well. The recommended "middle" scheme[J. Chem. Phys. 147 , 034109 (2017)] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation is proposed for understanding efficient stochastic thermostatting processes with molecular dynamics.     

Generalized principle of corresponding states and the scale invariant mean-field approach

In this paper we apply the relations between the critical points of the Lennard-Jones fluids and lattice gas model found in [V. L. Kulinskii, J. Phys. Chem. B 114, 2852 (2010)] to other short-ranged potentials like Buckingham and the Mie-potentials. The estimates for the corresponding critical point loci correlate quite satisfactory with the available numerical data for these potentials. The explanation for the correlation between the value of the second virial coefficient at the critical temperature and the particle volume found in [G. A. Vliegenthart and H. N. W. Lekkerkerker, J. Chem. Phys. 112, 5364 (2000)] is proposed. The connection of the stability of the liquid phase with the short range character of the potentials is discussed on the basis of the global isomorphism approach.     

Communication: Thermodynamic scaling of the Debye process in primary alcohols

The molecular dynamics of hydrogen-bonded liquids usually does not satisfy the thermodynamic scaling. However, very recently, two opposite conclusions about validity of thermodynamical scaling in monohydroxy alcohol, 2-ethyl-1-hexanol, were presented by Reiser et al. [J. Chem. Phys. 132, 181101 (2010)] and Fragiadakis et al. [J. Chem. Phys. 132, 144505 (2010)]. In this communication we present new experimental results that can explain this ostensible contradiction.     

Thermodynamical and structural properties of imidazolium based ionic liquids from molecular simulation

We have performed molecular dynamics simulations to determine the densities and heat of vaporization as well as structural information for the 1-alkyl-3-methyl-imidazolium based ionic liquids [amim][Cl] and [amim][BF(4)] in the temperature range from 298 to 363 K. In this simulation study, we used an united atom model of Liu et al. [Phys. Chem. Chem. Phys. 8, 1096 (2006)] for the [emim(+)] and [bmim(+)] cations, which we have extended for simulation in [hmim]-ILs and combined with parameters of Canongia Lopes et al. [J. Phys. Chem. B 108, 2038 (2004)] for the [Cl(-)] anion. Our simulation results prove that both the original united atoms approach by Liu et al. and our extension yield reasonable predictions for the ionic liquid with a considerably reduced computational expense than that required for all atoms models. Radial distribution functions and spatial distribution functions where employed to analyze the local structure of this ionic liquid, and in which way it is influenced by the type of the anion, the size of the cation, and the temperature. Our simulations give evidence for the occurrence of tail aggregations in these ionic liquids with increasing length of the side chain and also increasing temperature.     

Molecular weight dependence of polystyrene segmental dynamics in dilute blends with poly(vinyl methyl ether)

The segmental dynamics of backbone‐deuterated polystyrenes (d₃PS) with varying molecular weights (1.7–67 kg/mol) have been measured in blends with poly(vinyl methyl ether) (PVME). ²H NMR T₁ values at 15 and 77 MHz are reported for the pure d₃PS and for the dilute d₃PS component in PVME matrices. The temperature shift that is needed to superpose the NMR T₁ data for the pure d₃PS and the d₃PS as a dilute component in the blend ranges from 45 to 70 K. In the framework of Lodge/McLeish model, the self‐concentration value for d₃PS in these dilute blends with PVME is found to be independent of molecular weight. We thus establish for this system that the substantial influence of molecular weight on the blend segmental dynamics can be explained by homopolymer T_g differences. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2252–2262, 2007     

Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers

Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the order parameter, we find significant differences between the nucleation rates observed with the two dynamics, and between them and the standard Glauber dynamic [R. J. Glauber, J. Math. Phys. 4, 294 (1963)], which does not contain transition states. Our results show that great care must be exercised when devising kinetic Monte Carlo transition rates for specific physical or chemical systems.