The effect of functional groups on the glass transition temperature of atmospheric organic compounds: a molecular dynamics study.

Organic compounds constitute a substantial part of atmospheric particulate matter not only in terms of mass concentration but also in terms of distinct functional groups. The glass transition temperature provides an indirect way to investigate the phase state of the organic compounds, playing a crucial role in understanding their behavior and influence on aerosol processes. Molecular dynamics (MD) simulations were implemented here to predict the glass transition temperature (Tg) of atmospherically relevant organic compounds as well as the influence of their functional groups and length of their carbon chain. The cooling step used in the simulations was chosen to be neither too low (to supress crystallization) nor too high (to avoid Tg overprediction). According to the MD simulations, the predicted Tg is sensitive to the functional groups as follows: carboxylic acid (-COOH) > hydroxyl (-OH) and (-COOH) > carbonyls (-CO). Increasing the number of carbon atoms leads to higher Tg for the linearly structured compounds. Linear compounds with lower molecular weight were found to exhibit a lower Tg. No clear correlation between O : C and Tg was observed. The architecture of the carbon chain (linear, or branched, or ring) was also found to impact the glass transition temperature. Compounds containing a non-aromatic carbon ring are characterized by a higher Tg compared to linear and branched ones with the same number of carbon atoms.

Direct calculation of the functional inverse of realistic interatomic potentials in field-theoretic simulations.

We discuss the functional inverse problem in field-theoretic simulations for realistic pairwise potentials such as the Morse potential (widely used in particle simulations as an alternative to the 12-6 Lennard-Jones one), and we propose the following two solutions: (a) a numerical one based on direct inversion on a regular grid or deconvolution and (b) an analytical one by expressing attractive and repulsive contributions to the Morse potential as higher-order derivatives of the Dirac delta function; the resulting system of ordinary differential equations in the saddle-point approximation is solved numerically with appropriate model-consistent boundary conditions using a Newton-Raphson method. For the first time, exponential-like, physically realistic pair interactions are analytically treated and incorporated into a field-theoretic framework. The advantages and disadvantages of the two approaches are discussed in detail in connection with numerical findings from test simulations for the radial distribution function of a monatomic fluid at realistic densities providing direct evidence for the capability of the analytical method to resolve structural features down to the Angstrom scale.

Field-theoretic simulations beyond δ-interactions: Overcoming the inverse potential problem in auxiliary field models.

Modern field-theoretic simulations of complex fluids and polymers are constructed around a particle-to-field transformation that brings an inverse potential u-1 in the model equations. This has restricted the application of the framework to systems characterized by relatively simple pairwise interatomic interactions; for example, excluded volume effects are treated through the use of δ-function interactions. In this study, we first review available nonbonded pair interactions in field-theoretic models and propose a classification. Then, we outline the inverse potential problem and present an alternative approach on the basis of a saddle-point approximation, enabling the use of a richer set of pair interaction functions. We test our approach by using as an example the Morse potential, which finds extensive applications in particle-based simulations, and we calibrate u-1 with results from a molecular dynamics simulation. The u-1 thus obtained is consistent with the field-theoretic model equations, and when used in stand-alone self-consistent field simulations, it produces the correct fluid structure starting from a random initial state of the density field.

Molecular simulation of the high temperature phase behaviour of α-unsubstituted sexithiophene.

We examine the high-temperature phase behaviour of α-unsubstituted sexithiophene (α-6T) by means of Molecular Dynamics (MD) and Monte Carlo (MC) simulations using a recently developed state-of-the-art algorithm based on internal bridging moves. In the MD simulations, a realistic fully flexible united-atom model is used. In the MC simulations, a stiffer version of this united-atom model is implemented by restricting atoms on thiophene rings to remain strictly co-planar by employing holonomic constraints for all bond lengths and intra-ring bond bending angles; on the other hand, inter-ring torsion and bond bending angles are considered to be fully flexible subject to suitable potential energy functions. The MD simulations, which are started from the isotropic (Iso) phase at a relatively high temperature (above 700 K) and continued to lower temperatures under isobaric conditions using a very large simulation cell containing 8960 α-6T molecules, show four phase transitions: an isotropic-to-nematic (Iso-to-Nem) at 640 K, a nematic-to-smectic A (Nem-to-SmA) at 630 K, a smectic A-to-smectic C (SmA-to-SmC) at 620 K demonstrating smectic polymorphism, and a SmC-to-crystal-like (SmC-to-Cry) at 600 K. In the corresponding MC simulations, no Nem phase is observed; the system, as it is isobarically cooled down to lower temperatures from its Iso phase, undergoes directly a transition to a SmC phase at 690 K. This is attributed to the stiffer nature of the forcefield employed in these simulations. Both methods (MD and MC) shed light on the type and degree of molecular self-assembly, orientational and positional ordering as a function of temperature, and manifestation of liquid crystalline behaviour of α-6T. We provide a thorough characterization of structural ordering in all mesophases observed, in terms of several measures (radial correlation functions, orientational order parameters and X-ray diffraction patterns). According to the results, at the phase transition temperatures, drastic configurational changes take place driving α-6T molecules to positionally-ordered phases accompanied by self-assembly into characteristic layers which, in turn, are self-organized into macroscopic smectic phases. Our methodology opens up the way to exploring the rich phase behaviour and anisotropic ordering of the condensed phases of several longer (and perhaps more complex) thiophene-based polymers.

Mobility and settling rate of agglomerates of polydisperse nanoparticles.

Agglomerate settling impacts nanotoxicology and nanomedicine as well as the stability of engineered nanofluids. Here, the mobility of nanostructured fractal-like SiO2 agglomerates in water is investigated and their settling rate in infinitely dilute suspensions is calculated by a Brownian dynamics algorithm tracking the agglomerate translational and rotational motion. The corresponding friction matrices are obtained using the HYDRO++ algorithm [J. G. de la Torre, G. del Rio Echenique, and A. Ortega, J. Phys. Chem. B 111, 955 (2007)] from the Kirkwood-Riseman theory accounting for hydrodynamic interactions of primary particles (PPs) through the Rotne-Prager-Yamakawa tensor, properly modified for polydisperse PPs. Agglomerates are generated by an event-driven method and have constant mass fractal dimension but varying PP size distribution, mass, and relative shape anisotropy. The calculated diffusion coefficient from HYDRO++ is used to obtain the agglomerate mobility diameter dm and is compared with that from scaling laws for fractal-like agglomerates. The ratio dm/dg of the mobility diameter to the gyration diameter of the agglomerate decreases with increasing relative shape anisotropy. For constant dm and mean dp, the agglomerate settling rate, us, increases with increasing PP geometric standard deviation σp,g (polydispersity). A linear relationship between us and agglomerate mass to dm ratio, m/dm, is revealed and attributed to the fast Brownian rotation of such small and light nanoparticle agglomerates. An analytical expression for the us of agglomerates consisting of polydisperse PPs is then derived, us=1-ρfρpg3πµmdm (ρf is the density of the fluid, ρp is the density of PPs, µ is the viscosity of the fluid, and g is the acceleration of gravity), valid for agglomerates for which the characteristic rotational time is considerably shorter than their settling time. Our calculations demonstrate that the commonly made assumption of monodisperse PPs underestimates us by a fraction depending on σp,g and agglomerate mass mobility exponent. Simulations are in excellent agreement with deposition rate measurements of fumed SiO2 agglomerates in water.

Molecular dynamics simulation of the local concentration and structure in multicomponent aerosol nanoparticles under atmospheric conditions.

Molecular dynamics (MD) simulations were employed to investigate the local structure and local concentration in atmospheric nanoparticles consisting of an organic compound (cis-pinonic acid or n-C30H62), sulfate and ammonium ions, and water. Simulations in the isothermal-isobaric (NPT) statistical ensemble under atmospheric conditions with a prespecified number of molecules of the abovementioned compounds led to the formation of a nanoparticle. Calculations of the density profiles of all the chemical species in the nanoparticle, the corresponding radial pair distribution functions, and their mobility inside the nanoparticle revealed strong interactions developing between sulfate and ammonium ions. However, sulfate and ammonium ions prefer to populate the central part of the nanoparticle under the simulated conditions, whereas organic molecules like to reside at its outer surface. Sulfate and ammonium ions were practically immobile; in contrast, the organic molecules exhibited appreciable mobility at the outer surface of the nanoparticle. When the organic compound was a normal alkane (e.g. n-C30H62), a well-organized (crystalline-like) phase was rapidly formed at the free surface of the nanoparticle and remained separate from the rest of the species.

Determination of the effective diffusivity of water in a poly (methyl methacrylate) membrane containing carbon nanotubes using kinetic Monte Carlo simulations.

A kinetic Monte Carlo (kMC) simulation algorithm is developed for computing the effective diffusivity of water molecules in a poly(methyl methacrylate) (PMMA) matrix containing carbon nanotubes (CNTs) at several loadings. The simulations are conducted on a cubic lattice to the bonds of which rate constants are assigned governing the elementary jump events of water molecules from one lattice site to another. Lattice sites belonging to PMMA domains of the membrane are assigned different rates than lattice sites belonging to CNT domains. Values of these two rate constants are extracted from available numerical data for water diffusivity within a PMMA matrix and a CNT pre-computed on the basis of independent atomistic molecular dynamics simulations, which show that water diffusivity in CNTs is 3 orders of magnitude faster than in PMMA. Our discrete-space, continuum-time kMC simulation results for several PMMA-CNT nanocomposite membranes (characterized by different values of CNT length L and diameter D and by different loadings of the matrix in CNTs) demonstrate that the overall or effective diffusivity, D(eff), of water in the entire polymeric membrane is of the same order of magnitude as its diffusivity in PMMA domains and increases only linearly with the concentration C (vol. %) in nanotubes. For a constant value of the concentration C, D(eff) is found to vary practically linearly also with the CNT aspect ratio L/D. The kMC data allow us to propose a simple bilinear expression for D(eff) as a function of C and L/D that can describe the numerical data for water mobility in the membrane extremely accurately. Additional simulations with two different CNT configurations (completely random versus aligned) show that CNT orientation in the polymeric matrix has only a minor effect on D(eff) (as long as CNTs do not fully penetrate the membrane). We have also extensively analyzed and quantified sublinear (anomalous) diffusive phenomena over small to moderate times and correlated them with the time needed for penetrant water molecules to explore the available large, fast-diffusing CNT pores before Fickian diffusion is reached.

Accurate prediction of the linear viscoelastic properties of highly entangled mono and bidisperse polymer melts.

We present a hierarchical computational methodology which permits the accurate prediction of the linear viscoelastic properties of entangled polymer melts directly from the chemical structure, chemical composition, and molecular architecture of the constituent chains. The method entails three steps: execution of long molecular dynamics simulations with moderately entangled polymer melts, self-consistent mapping of the accumulated trajectories onto a tube model and parameterization or fine-tuning of the model on the basis of detailed simulation data, and use of the modified tube model to predict the linear viscoelastic properties of significantly higher molecular weight (MW) melts of the same polymer. Predictions are reported for the zero-shear-rate viscosity η0 and the spectra of storage G'(ω) and loss G″(ω) moduli for several mono and bidisperse cis- and trans-1,4 polybutadiene melts as well as for their MW dependence, and are found to be in remarkable agreement with experimentally measured rheological data.

Detailed atomistic simulation of the nano-sorption and nano-diffusivity of water, tyrosol, vanillic acid, and p-coumaric acid in single wall carbon nanotubes.

We report results from a detailed computer simulation study for the nano-sorption and mobility of four different small molecules (water, tyrosol, vanillic acid, and p-coumaric acid) inside smooth single-wall carbon nanotubes (SWCNTs). Most of the results have been obtained with the molecular dynamics (MD) method, but especially for the most narrow of the CNTs considered, the results for one of the molecules addressed here (water) were further confirmed through an additional Grand Canonical (µVT) Monte Carlo (GCMC) simulation using a value for the water chemical potential µ pre-computed with the particle deletion method. Issues addressed include molecular packing and ordering inside the nanotube for the four molecules, average number of sorbed molecules per unit length of the tube, and mean residence time and effective axial diffusivities, all as a function of tube diameter and tube length. In all cases, a strong dependence of the results on tube diameter was observed, especially in the way the different molecules are packed and organized inside the CNT. For water for which predictions of properties such as local structure and packing were computed with both methods (MD and GCMC), the two sets of results were found to be fully self-consistent for all types of SWCNTs considered. Water diffusivity inside the CNT (although, strongly dependent on the CNT diameter) was computed with two different methods, both of which gave identical results. For large enough CNT diameters (larger than about 13 Å), this was found to be higher than the corresponding experimental value in the bulk by about 55%. Surprisingly enough, for the rest of the molecules simulated (phenolic), the simulations revealed no signs of mobility inside nanotubes with a diameter smaller than the (20, 20) tube. This is attributed to strong phenyl-phenyl attractive interactions, also to favorable interactions of these molecules with the CNT walls, which cause them to form highly ordered, very stable structures inside the nanotube, especially under strong confinement. The interaction, in particular, of the methyl group (present in tyrosol, vanillic acid, and p-coumaric acid) with the CNT walls seems to play a key role in all these compounds causing them to remain practically immobile inside nanotubes characterized by diameters smaller than about 26 Å. It is only for larger-diameter CNTs that tyrosol, vanillic acid, and p-coumaric acid were observed to demonstrate appreciable mobility.

Geometric Analysis of Free and Accessible Volume in Atmospheric Nanoparticles.

Computer-generated atomistic microstructures of atmospheric nanoparticles are geometrically analyzed using Delaunay tessellation followed by Monte Carlo integration to compute their free and accessible volume. The nanoparticles studied consist of cis-pinonic acid (a biogenic organic aerosol component), inorganic ions (sulfate and ammonium), and water. Results are presented for the free or unoccupied volume in different domains of the nanoparticles and its dependence on relative humidity and organic content. We also compute the accessible volume to small penetrants such as water molecules. Most of the free volume or volume accessible to a penetrant as large as a water molecule is located in the domains occupied by organics. In contrast, regions dominated by inorganics do not have any cavities with sizes larger than 1 Å. Solid inorganic domains inside the particle are practically impermeable to any small molecule, thereby offering practically infinite resistance to diffusion. A guest molecule can find diffusive channels to wander around within the nanoparticle only through the aqueous and organic-rich domains. The largest pores are observed in nanoparticles with high levels of organic mass and low relative humidity. At high relative humidity, the presence of more water molecules reduces the empty space in the inner domains of the nanoparticle, since areas rich in organic molecules (which are the only ones where appreciable pores are found) are pushed to the outer area of the particle. This, however, should not be expected to affect the diffusive process as transport through the aqueous phase inside the particle will be, by default, fast due to its fluid-like nature.

Excluded-Volume Interactions in Field-Theoretic Simulations: Multiconvolutions and Model Equivalence.

To deal with divergences of functional integrals in field-theoretic simulations (FTS) of complex fluids, the microscopic density is often smeared by being replaced by a convoluted one, typically using a Gaussian masking function. The smearing changes radically the nature of nonbonded interactions of the original microscopic density and results in a regularized model that is free of ultraviolet (UV) divergences. In this work, we first resolve a few fundamental issues related with the use of masking functions for δ-interactions in FTS and then we detail a new methodology that builds on the concept of multiconvoluted inverse potentials and a principle of model equivalence for statistical weights to accommodate more physically relevant interactions in FTS. The capabilities of the new approach are highlighted by examining the Gaussian-regularized Edwards model (GREM) and the Yukawa potential. A successful test calculation of the excess chemical potential of a polymer chain in a good solvent with the GREM illustrates the power of the new theoretical framework.

Coarse-Grained Model Incorporating Short- and Long-Range Effective Potentials for the Fast Simulation of Micelle Formation in Solutions of Ionic Surfactants.

A coarse-grained model comprising short- and long-range effective potentials, parametrized with the iterative Boltzmann inversion (IBI) method, is presented for capturing micelle formation in aqueous solutions of ionic surfactants using as a model system sodium dodecyl sulfate (SDS). In the coarse-grained (CG) model, each SDS molecule is represented as a sequence of four beads while each water molecule is modeled as a single bead. The proposed CG scheme involves ten potential energy functions: four of them describe bonded interactions and control the distribution functions of intramolecular degrees of freedom (bond lengths, valence angles, and dihedrals) along an SDS molecule while the other six account for intermolecular interactions between pairs of SDS and water beads and control the radial distribution functions. The nonbonded effective potentials between coarse-grained SDS molecules extend up to about 12 nm and capture structural and morphological features of the micellar solution both at short and long distances. The long-range component of these potentials, in particular, captures correlations between surfactant molecules belonging to different micelles and is essential to describe ordering associated with micelle formation. A new strategy is introduced for determining the effective potentials through IBI by using information (target distribution functions) extracted from independent atomistic simulations of a micellar reference system (a salt-free SDS solution at total surfactant concentration cT equal to 103 mM, temperature T equal to 300 K, and pressure P equal to 1 atm) obtained through a multiscale approach described in an earlier study. It employs several optimization steps for bonded and nonbonded interactions and a gradual parametrization of the short- and long-range components of the latter, followed by reparametrization of the bonded ones. The proposed CG model can reproduce remarkably accurately the microstructure and morphology of the reference system within only a few hours of computational time. It is therefore very promising for future studies of structural and morphological behavior of various liquid surfactant formulations.

Structure and Dynamics of Highly Attractive Polymer Nanocomposites in the Semi-Dilute Regime: The Role of Interfacial Domains and Bridging Chains.

Detailed molecular dynamics (MD) simulations are employed to study how the presence of adsorbed domains and nanoparticle bridging chains affect the structural, conformational, thermodynamic, and dynamic properties of attractive polymer nanocomposite melts in the semi-dilute regime. As a model system we have chosen an unentangled poly(ethylene glycol) (PEG) matrix containing amorphous spherical silica nanoparticles with different diameters and at different concentrations. Emphasis is placed on properties such as the polymer mass density profile around nanoparticles, the compressibility of the system, the mean squared end-to-end distance of PEG chains, their orientational and diffusive dynamics, the single chain form factor, and the scattering functions. Our analysis reveals a significant impact of the adsorbed, interfacial polymer on the microscopic dynamic and conformational properties of the nanocomposite, especially under conditions favoring higher surface-to-volume ratios (e.g., for small nanoparticle sizes at fixed nanoparticle loading, or for higher silica concentrations). Simultaneously, adsorbed polymer chains adopt graft-like conformations, a feature that allows them to considerably extend away from the nanoparticle surface to form bridges with other nanoparticles. These bridges drive the formation of a nanoparticle network whose strength (number of tie chains per nanoparticle) increases substantially with increasing concentration of the polymer matrix in nanoparticles, or with decreasing nanoparticle size at fixed nanoparticle concentration. The presence of hydroxyl groups at the ends of PEG chains plays a key role in the formation of the network. If hydroxyl groups are substituted by methoxy ones, the simulations reveal that the number of bridging chains per nanoparticle decreases dramatically, thus the network formed is less dense and less strong mechanically, and has a smaller impact on the properties of the nanocomposite. Our simulations predict further that the isothermal compressibility and thermal expansion coefficient of PEG-silica nanocomposites are significantly lower than those of pure PEG, with their values decreasing practically linear with increasing concentration of the nanocomposite in nanoparticles.

Tension thickening, molecular shape, and flow birefringence of an H-shaped polymer melt in steady shear and planar extension.

Despite recent advances in the design of extensional rheometers optimized for strain and stress controlled operation in steady, dynamic, and transient modes, obtaining reliable steady-state elongational data for macromolecular systems is still a formidable task, limiting today's approach to trial-and-error efforts rather than based on a deep understanding of the deformation processes occurring under elongation. Guided, in particular, by the need to understand the special rheology of branched polymers, we studied a model, unentangled H-shaped polyethylene melt using nonequilibrium molecular dynamics simulations based on a recently developed rigorous statistical mechanics algorithm. The melt has been simulated under steady shear and steady planar extension, over a wide range of deformation rates. In shear, the steady-state shear viscosity is observed to decrease monotonically as the shear rate increases; furthermore, the degree of shear thinning of the viscosity and of the first- and second-normal stress coefficients is observed to be similar to that of a linear analog of the same total chain length. By contrast, in planar extension, the primary steady-state elongational viscosity eta(1) is observed to exhibit a tension-thickening behavior as the elongation rate epsilon increases, which we analyze here in terms of (a) perturbations in the instantaneous intrinsic chain shape and (b) differences in the stress distribution along chain contour. The maximum in the plot of eta(1) with epsilon occurs when the arm-stretching mode becomes active and is followed by a rather abrupt tension-thinning behavior. In contrast, the second elongational viscosity eta(2) shows only a tension-thinning behavior. As an interesting point, the simulations predict the same value for the stress optical coefficient in the two flows, revealing an important rheo-optical characteristic. In agreement with experimental indications on significantly longer systems, our results confirm the importance of chain branching on the unique rheological properties of polymer melts in extension.

Quantifying chain reptation in entangled polymer melts: topological and dynamical mapping of atomistic simulation results onto the tube model.

The topological state of entangled polymers has been analyzed recently in terms of primitive paths which allowed obtaining reliable predictions of the static (statistical) properties of the underlying entanglement network for a number of polymer melts. Through a systematic methodology that first maps atomistic molecular dynamics (MD) trajectories onto time trajectories of primitive chains and then documents primitive chain motion in terms of a curvilinear diffusion in a tubelike region around the coarse-grained chain contour, we are extending these static approaches here even further by computing the most fundamental function of the reptation theory, namely, the probability psi(s,t) that a segment s of the primitive chain remains inside the initial tube after time t, accounting directly for contour length fluctuations and constraint release. The effective diameter of the tube is independently evaluated by observing tube constraints either on atomistic displacements or on the displacement of primitive chain segments orthogonal to the initial primitive path. Having computed the tube diameter, the tube itself around each primitive path is constructed by visiting each entanglement strand along the primitive path one after the other and approximating it by the space of a small cylinder having the same axis as the entanglement strand itself and a diameter equal to the estimated effective tube diameter. Reptation of the primitive chain longitudinally inside the effective constraining tube as well as local transverse fluctuations of the chain driven mainly from constraint release and regeneration mechanisms are evident in the simulation results; the latter causes parts of the chains to venture outside their average tube surface for certain periods of time. The computed psi(s,t) curves account directly for both of these phenomena, as well as for contour length fluctuations, since all of them are automatically captured in the atomistic simulations. Linear viscoelastic properties such as the zero shear rate viscosity and the spectra of storage and loss moduli obtained on the basis of the obtained psi(s,t) curves for three different polymer melts (polyethylene, cis-1,4-polybutadiene, and trans-1,4-polybutadiene) are consistent with experimental rheological data and in qualitative agreement with the double reptation and dual constraint models. The new methodology is general and can be routinely applied to analyze primitive path dynamics and chain reptation in atomistic trajectories (accumulated through long MD simulations) of other model polymers or polymeric systems (e.g., bidisperse, branched, grafted, etc.); it is thus believed to be particularly useful in the future in evaluating proposed tube models and developing more accurate theories for entangled systems.

Effect of pH and Molecular Length on the Structure and Dynamics of Linear and Short-Chain Branched Poly(ethylene imine) in Dilute Solution: Scaling Laws from Detailed Molecular Dynamics Simulations.

Atomistic molecular dynamics (MD) simulations are carried out to examine the effect of molecular weight Mw (= 0.6, 0.86, 1.12, and 2.15 kDa) and pH (or equivalently, degree of ionization, α+ = 0, 50, and 100%) on the structure, state of hydration, and dynamics of linear and branched poly(ethylene imine) (PEI) chains in infinitely dilute salt-free aqueous solutions. It is found that the degree of ionization is the key factor determining the type of molecular conformation adopted by PEI, regardless of molecular architecture and chain length, resulting in a stable trans conformation for fully ionized solutions and in a stable gauche+/gauche- state for neutral or alternate ionized ones; in the latter case, a strong electrolyte behavior is verified for both linear and branched PEI. Linear PEI is observed to be significantly stiffer than branched PEI of the same molecular weight at 100% degree of ionization, but the effect subsides as the degree of ionization decreases. Also, linear PEI diffuses markedly slower than branched PEI of the same Mw. From the MD results, scaling exponents are deduced and reported for the conformation, solvent-accessible surface area, and dynamics of the two different PEI structures with Mw.

Effect of Polymer Concentration on the Structure and Dynamics of Short Poly(N,N-dimethylaminoethyl methacrylate) in Aqueous Solution: A Combined Experimental and Molecular Dynamics Study.

A combined experimental and molecular dynamics (MD) study is performed to investigate the effect of polymer concentration on the zero shear rate viscosity η0 of a salt-free aqueous solution of poly(N,N-dimethylaminoethyl methacrylate) (PDMAEMA), a flexible thermoresponsive weak polyelectrolyte with a bulky 3-methyl-1,1-diphenylpentyl unit as the terminal group. The study is carried out at room temperature (T = 298 K) with relatively short PDMAEMA chains (each containing N = 20 monomers or repeat units) at a fixed degree of ionization (α+ = 100%). For the MD simulations, a thorough validation of several molecular mechanics force fields is first undertaken for assessing their capability to accurately reproduce the experimental observations and established theoretical laws. The generalized Amber force field in combination with the restrained electrostatic potential charge fitting method is eventually adopted. Three characteristic concentration regimes are considered: the dilute (from 5 to 10 wt %), the semidilute (from 10 to 20 wt %), and the concentrated (from 20 to 29 wt %); the latter two are characterized by polymer concentrations cp higher than the characteristic overlap concentration cp*. The structural behavior of the PDMAEMA chains in the solution is assessed by calculating the square root of their mean-square radius of gyration ⟨Rg2⟩0.5, the square root of the average square chain end-to-end distance ⟨Ree2⟩0.5, the ratio ⟨Ree2⟩/⟨Rg2⟩, and the persistence length Lp. It is observed that at low polymer concentrations, PDMAEMA chains adopt a stiffer and slightly extended conformation because of excluded-volume effects (a good solvent is considered in this study) and electrostatic repulsions within the polymer chains. As the polymer concentration increases above 20 wt %, the PDMAEMA chains adopt more flexible conformations, as the excluded-volume effects seize and the charge repulsion within the polymer chains subsides. The effect of total polymer concentration on PDMAEMA chain dynamics in the solution is assessed by calculating the orientational relaxation time τc of the chain, the center-of-mass diffusion coefficient D, and the zero shear rate viscosity η0; the latter is also measured experimentally here and found to be in excellent agreement with the MD predictions.

Dynamic Heterogeneity in Ring-Linear Polymer Blends.

We present results from a direct statistical analysis of long molecular dynamics (MD) trajectories for the orientational relaxation of individual ring molecules in blends with equivalent linear chains. Our analysis reveals a very broad distribution of ring relaxation times whose width increases with increasing ring/linear molecular length and increasing concentration of the blend in linear chains. Dynamic heterogeneity is also observed in the pure ring melts but to a lesser extent. The enhanced degree of dynamic heterogeneity in the blends arises from the substantial increase in the intrinsic timescales of a large subpopulation of ring molecules due to their involvement in strong threading events with a certain population of the linear chains present in the blend. Our analysis suggests that the relaxation dynamics of the rings are controlled by the different states of their threading by linear chains. Unthreaded or singly-threaded rings exhibit terminal relaxation very similar to that in their own melt, but multiply-threaded rings relax much slower due to the long lifetimes of the corresponding topological interactions. By further analyzing the MD data for ring molecule terminal relaxation in terms of the sum of simple exponential functions we have been able to quantify the characteristic relaxation times of the corresponding mechanisms contributing to ring relaxation both in their pure melts and in the blends, and their relative importance. The extra contribution due to ring-linear threadings in the blends becomes immediately apparent through such an analysis.

Quantitative Prediction of the Structure and Viscosity of Aqueous Micellar Solutions of Ionic Surfactants: A Combined Approach Based on Coarse-Grained MARTINI Simulations Followed by Reverse-Mapped All-Atom Molecular Dynamics Simulations.

We address the problem of the quantitative prediction of micelle formation in dilute aqueous solutions of ionic surfactants using sodium dodecyl sulfate (SDS) as a model system through a computational approach that involves three steps: (a) execution of coarse-grained simulations based on the MARTINI force field (with slightly modified parameters to afford the formation of large micelles); (b) reverse mapping of the final self-assembled coarse-grained configuration into an all-atom configuration; and (c) final relaxation of this all-atom configuration through short-time (on the order of a few tens of nanoseconds), detailed isothermal-isobaric molecular dynamics simulations using the CHARMM36 force field. For a given concentration of the solution in SDS molecules, the modified MARTINI-based coarse-grained simulations lead to the formation of large micelles characterized by mean aggregation numbers above the experimentally observed ones. However, by reintroducing the detailed chemical structure through a strategy that solves a well-defined geometric problem and re-equilibrating, these large micellar aggregates quickly dissolve to smaller ones and equilibrate to sizes that perfectly match the average micelle size measured experimentally at the given surfactant concentration. From the all-atom molecular dynamics simulations, we also deduce the surfactant diffusivity DSDS and the zero-shear rate viscosity, η0, of the solution, which are observed to compare very favorably with the few experimental values that we were able to find in the literature.

Effect of pH and Molecular Length on the Structure and Dynamics of Short Poly(acrylic acid) in Dilute Solution: Detailed Molecular Dynamics Study.

Long MD simulations are carried out using a detailed all-atom force field to investigate the effect of pH or, equivalently, degree of ionization α- (= 0, 50, 100%) and degree of polymerization N (= 20, 23, 46, 70, and 110) on the structure and dynamics of poly(acrylic acid) (PAA) at infinite dilution. To ensure the validity and add to the reliability of our research conclusions, a systematic validation of several molecular mechanics force fields is performed. It is observed that the generalized AMBER force field in combination with the RESP charge fitting method best describes both the structural and dynamical behavior of PAA in comparison to experimentally obtained data. It is found that ⟨ Rg2⟩0.5changes with N as ⟨ Rg2⟩0.5 ∼ Nν, with ν = 0.27 at α- = 0% degree of ionization (acidic conditions), ν = 0.94 at α- = 50% degree of ionization (neutral conditions), and ν = 0.87 at α- = 100% degree of ionization (basic conditions), which is in perfect agreement with theory. The global shape of the PAA chain in the solution is quantified in terms of the three eigenvalues of the average radius-of-gyration tensor, the relative shape anisotropy κ2, and the asphericity parameter b. It is revealed that at α- = 0%, the chain adopts a spherelike conformation, while at α- = 50 and 100%, its conformation is flattened and flexible. In addition, it is revealed that as the degree of ionization increases, the persistence length Lp increases, which suggests that PAA chains become stiffer with increasing pH. The global and local conformational changes of the PAA chain with the degree of ionization are found to be highly related to the solvation of the polymer. Finally, it is revealed that the diffusion coefficient D of the center of mass of PAA also exhibits a power law scaling with N, D ∼ Nν, with ν = 0.25 at α- = 0% degree of ionization, ν = 0.46 at α- = 50% degree of ionization (neutral conditions), and ν = 0.44 at α- = 100% degree of ionization (basic conditions), in excellent agreement with recent experimental data and theoretical predictions.