Effect of solvent quality on the conformation and relaxation of polymers via dissipative particle dynamics

Non-Newtonian dynamics modelled with non-linear transport coefficients at the mesoscale by using dissipative particle dynamics

We derive the algorithms for the dynamics of the standard dissipative particle dynamics model (DPD) for a velocity-dependent friction coefficient. By introducing simple estimators of the local rate of strain we propose an interparticle friction coefficient that decreases for high deformation rates, eventually leading to the macroscopic shear-thinning behaviour. We have derived the appropriate fluctuation-dissipation theorems that include the correction of the spurious behaviour due to the coupling of the non-linear friction and the fluctuations. The consistency of the model has been numerically investigated, including the Maxwell-Boltzmann distribution for the particle velocities as well as the comparison with the standard linear model for various stresses. The shear-thinning behaviour is clearly reported. Finally, along with the important methodological aspects related to the derivation of the algorithms for non-linear interparticle friction, we introduce a novel two-step algorithm that permits us the integration of the dynamic equations of the DPD model without the explicit derivation of the corrective terms due to the spurious behaviour.

Exploring conformations of comb-like polymers with varying grafting density in dilute solutions

Comb-like polymers have shown potential as advanced materials for a diverse palette of applications due to the tunability of their polymer architecture. To date, however, it still remains a challenge to understand how the conformational properties of these polymers arise from the interplay of their architectural parameters. In this work, extensive simulations were performed using dissipative particle dynamics to investigate the effect of grafting density, backbone length, and sidechain length on the conformations of comb-like polymers immersed in a good solvent. To quantify the effect of these architectural parameters on polymer conformations, we computed the asphericity, radius of gyration, and backbone and sidechain end-to-end distances. Bond-bond correlation functions and effective Kuhn lengths were computed to quantify the topological stiffness induced by sidechain-sidechain interactions. Simulation results reveal that the effective Kuhn length increases as grafting density and sidechain length increase, in agreement with previous experimental and theoretical studies. This increase in stiffness results in comb-like polymers adopting extended conformations as grafting density and sidechain length increase. Simulation results regarding the radius of gyration of comb-like polymers as a function of grafting density are compared with scaling theory predictions based on a free energy proposed by Morozova and Lodge [ACS Macro Lett. 6, 1274-1279 (2017)] and scaling arguments by Tang et al. [Macromolecules 55, 8668-8675 (2022)].

Dissipative particle dynamics simulations in colloid and Interface science: a review

Dissipative particle dynamics (DPD) is one of the most efficient mesoscale coarse-grained methodologies for modeling soft matter systems. Here, we comprehensively review the progress in theoretical formulations, parametrization strategies, and applications of DPD over the last two decades. DPD bridges the gap between the microscopic atomistic and macroscopic continuum length and time scales. Numerous efforts have been performed to improve the computational efficiency and to develop advanced versions and modifications of the original DPD framework. The progress in the parametrization techniques that can reproduce the engineering properties of experimental systems attracted a lot of interest from the industrial community longing to use DPD to characterize, help design and optimize the practical products. While there are still areas for improvements, DPD has been efficiently applied to numerous colloidal and interfacial phenomena involving phase separations, self-assembly, and transport in polymeric, surfactant, nanoparticle, and biomolecules systems.

Decagram scale production of deuterated mineral oil and polydecene as solvents for polymer studies in neutron scattering

Decagram scale syntheses of deuterated mineral oil (d-MO) and poly(1-decene) (d-PD) were achieved by direct catalytic hydrothermal H/D exchange reaction in D₂O.

Dissipative particle dynamics of diffusion-NMR requires high Schmidt-numbers

We present an efficient mesoscale model to simulate the diffusion measurement with nuclear magnetic resonance (NMR). On the level of mesoscopic thermal motion of fluid particles, we couple the Bloch equations with dissipative particle dynamics (DPD). Thereby we establish a physically consistent scaling relation between the diffusion constant measured for DPD-particles and the diffusion constant of a real fluid. The latter is based on a splitting into a centre-of-mass contribution represented by DPD, and an internal contribution which is not resolved in the DPD-level of description. As a consequence, simulating the centre-of-mass contribution with DPD requires high Schmidt numbers. After a verification for fundamental pulse sequences, we apply the NMR-DPD method to NMR diffusion measurements of anisotropic fluids, and of fluids restricted by walls of microfluidic channels. For the latter, the free diffusion and the localisation regime are considered.

Universal shape characteristics for the mesoscopic polymer chain via dissipative particle dynamics

In this paper we study the shape characteristics of a polymer chain in a good solvent using a mesoscopic level of modelling. The dissipative particle dynamics simulations are performed in 3D space at a range of chain lengths N. The scaling laws for the end-to-end distance and gyration radius are examined first and found to hold for [Formula: see text] yielding a reasonably accurate value for the Flory exponent ν. Within the same interval of chain lengths, the asphericity, prolateness and some other shape characteristics of the chain are found to become independent of N. Their mean values are found to agree reasonably well with the respective theoretical results and lattice Monte Carlo (MC) simulations. We found the probability distribution for a wide range of shape characteristics. For the asphericity and prolateness they are quite broad, resembling in form the results of lattice MC simulations. By means of the analytic fitting of these distributions, the most probable values for the shape characteristics are found to supplement their mean values.

Multiscale simulation of ideal mixtures using smoothed dissipative particle dynamics

Smoothed dissipative particle dynamics (SDPD) [P. Español and M. Revenga, Phys. Rev. E 67, 026705 (2003)] is a thermodynamically consistent particle-based continuum hydrodynamics solver that features scale-dependent thermal fluctuations. We obtain a new formulation of this stochastic method for ideal two-component mixtures through a discretization of the advection-diffusion equation with thermal noise in the concentration field. The resulting multicomponent approach is consistent with the interpretation of the SDPD particles as moving volumes of fluid and reproduces the correct fluctuations and diffusion dynamics. Subsequently, we provide a general multiscale multicomponent SDPD framework for simulations of molecularly miscible systems spanning length scales from nanometers to the non-fluctuating continuum limit. This approach reproduces appropriate equilibrium properties and is validated with simulation of simple one-dimensional diffusion across multiple length scales.

Hydrodynamic Interactions and Entanglements of Polymer Solutions in Many-Body Dissipative Particle Dynamics

Using many-body dissipative particle dynamics (MDPD), polymer solutions with concentrations spanning dilute and semidilute regimes are modeled. The parameterization of MDPD interactions for systems with liquid⁻vapor coexistence is established by mapping to the mean-field Flory⁻Huggins theory. The characterization of static and dynamic properties of polymer chains is focused on the effects of hydrodynamic interactions and entanglements. The coil⁻globule transition of polymer chains in dilute solutions is probed by varying solvent quality and measuring the radius of gyration and end-to-end distance. Both static and dynamic scaling relations for polymer chains in poor, theta, and good solvents are in good agreement with the Zimm theory with hydrodynamic interactions considered. Semidilute solutions with polymer volume fractions up to 0.7 exhibit the screening of excluded volume interactions and subsequent shrinking of polymer coils. Furthermore, entanglements become dominant in the semidilute solutions, which inhibit diffusion and relaxation of chains. Quantitative analysis of topology violation confirms that entanglements are correctly captured in the MDPD simulations.

Effect of chain chirality on the self-assembly of sickle hemoglobin

We present simulation results on the self-assembly behavior of sickle hemoglobin (HbS). A coarse-grained HbS model, which contains hydrophilic and hydrophobic particles explicitly, is constructed to match the structural properties and physical description of HbS. The hydrophobic interactions are shown to be necessary with chirality being the main driver for the formation of HbS fibers. In the absence of chain chirality, only small self-assembled aggregates are observed whereas self-assembled elongated steplike bundle microstructures appear when we include chain chirality. We also investigate the effect of confinement on self-assembly, and find that elongated fibers-similar to open-space ones-can be obtained in hard confinement domains but cannot be formed within compliant red blood cell (RBC) domains under the same assumptions. We show, however, that by placing explicitly HbS fibers inside the RBCs and subjecting them to linear elongation and bending, we obtain different types of sickle-shaped RBCs as observed in sickle cell anemia.

Dissipative particle dynamics simulations on inversion dynamics of spherical micelles

We simulate the inversion process of a spherical micelle composed of symmetric diblock copolymers by means of dissipative particle dynamics. The evolution of micelle morphology reveals that the inversion is a two-staged process, in which a rapid agglomeration of outer lyophobic blocks occurs first, followed by a slow penetration of inner lyophilic blocks through the porous lyophobic layer. Calculation of the radius of gyration and hydrodynamic radius indicates that an intermediate with a dilute core and a dense shell emerges in the inversion. The characteristic time of inversion scales with the block copolymer chain length with the scaling exponent ranging from 1.67 to 1.89, which can be well described by a simplified chemical-potential-driven flow model. Further simulations incorporating different denaturation times for the two types of blocks indicate the inversions do not experience molecularly scattered states, but form either collapsed intermediates or loosely associated clusters of small sizes. Possible connections of the simulations to the light scattering experiments are discussed.

Simulation of dilute solutions of linear and star-branched polymers by dissipative particle dynamics

A most promising off-lattice technique in order to simulate not only static but in addition dynamic behavior of linear and star-branched chains is the dissipative particle dynamics (DPD) method. In this model the atomistic representation of polymer molecules is replaced by a (coarse-grained) equivalent chain consisting of beads which are repulsive for each other in order to mimic the excluded volume effect (successive beads in addition are linked by springs). Likewise solvent molecules are combined to beads which in turn are repulsive for each other as well as for the polymer segments. The system is relaxed by molecular dynamics solving Newton's laws under the influence of short ranged conservative forces (i.e., repulsion between nonbonded beads and a proper balance of repulsion and attraction between bonded segments) and dissipative forces due to friction between particles, the latter representing the thermostat in conjunction with proper random forces. A variation of the strength of the repulsion between different types of beads allows the simulation of any desired thermodynamic situation. Static and dynamic properties of isolated linear and star-branched chains embedded in athermal, exothermal, and endothermal solvent are presented and theta conditions are examined. The generally accepted scaling concept for athermal systems is fairly well reproduced by linear and star-branched DPD chains and theta conditions appear for a unique parameter independent of functionality as in the case of Monte Carlo simulations. Furthermore, the correspondence between DPD and Monte Carlo data referring to the shape of chains and stars is fairly well, too. For dilute solutions the Zimm behavior is expected for dynamic properties which is indeed realized in DPD systems.

The coordination of protein motors and the kinetic behavior of microtubule — A computational study

Utilizing the mechanical energy converted from chemical energy through hydrolysis of ATP, motor proteins drive cytoskeleton filaments to move in various biological systems. Recent technological advance has shown the potential of the motor proteins for powering future nano-bio-mechanical systems. In order to effectively use motor proteins as a biological motor, the interaction between the protein motors and bio-filaments needs to be well clarified, since such interaction is largely influenced by many factors, such as the coordination among the motors, their dynamic behavior, physical properties of microtubules, and the viscosity of solution involved, etc. In this study, a two-dimensional model was proposed to simulate the motion of a microtubule driven by protein motors based on a dissipative particle dynamics (DPD) method with attempt to correlate the microtubule's kinetic behavior to the coordination among protein motors.

Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics

The authors analyzed extensively the dynamics of polymer chains in solutions simulated with dissipative particle dynamics (DPD), with a special focus on the potential influence of a low Schmidt number of a typical DPD fluid on the simulated polymer dynamics. It has been argued that a low Schmidt number in a DPD fluid can lead to underdevelopment of the hydrodynamic interaction in polymer solutions. The authors' analyses reveal that equilibrium polymer dynamics in dilute solution, under typical DPD simulation conditions, obey the Zimm [J. Chem. Phys. 24, 269 (1956)] model very well. With a further reduction in the Schmidt number, a deviation from the Zimm model to the Rouse model is observed. This implies that the hydrodynamic interaction between monomers is reasonably developed under typical conditions of a DPD simulation. Only when the Schmidt number is further reduced, the hydrodynamic interaction within the chains becomes underdeveloped. The screening of the hydrodynamic interaction and the excluded volume interaction as the polymer volume fraction is increased are well reproduced by the DPD simulations. The use of soft interaction between polymer beads and a low Schmidt number do not produce noticeable problems for the simulated dynamics at high concentrations, except for the entanglement effect which is not captured in the simulations.

Dissipative particle dynamics study on the interfaces in incompatible A/B homopolymer blends and with their block copolymers

Dissipative particle dynamics, a simulation technique appropriate at mesoscopic scales, has been applied to investigate the interfaces in immiscible binary A/B homopolymer blends and in the ternary systems with their block copolymers. For the binary blends, the interfacial tension increases and the interface thickness decreases with increasing Flory-Huggins interaction parameter chi while the homopolymer chain length is fixed. However, when the chi parameter and one of the homopolymer chain length is fixed, increasing another homopolymer chain length will induce only a small increase on interfacial tension and slight decrease on interface thickness. For the ternary blends, adding the A-b-B block copolymer will reduce the interfacial tension. When the mole number of the block copolymer is fixed, longer block chains have higher efficiency on reducing the interfacial tension than the shorter ones. But for the block copolymers with fixed volume fraction, shorter chains will be more efficient than the longer ones on reducing the interfacial tension. Increasing the block copolymer concentration reduces interfacial tension. This effect is more prominent for shorter block copolymer chains.

Dissipative-particle-dynamics model for two-phase flows

Dissipative particle dynamics (DPD) is a mesoscopic method in which coarse graining is done at the molecular level to capture the physics at the meso level. In this paper, we present a DPD model for two-phase flows involving liquid and vapor phases. The model is based on mean-field theory. Phase segregation between the two phases is simulated by the choice of an equation of state with a van der Waals loop. Surface tension is modeled by a term that depends on higher-order density gradients and accounts for long-range attractive forces. To test the model, we present results from simulations of a liquid layer, several liquid cylinders of varying size to verify the Laplace's law, small- and large-amplitude liquid cylinder oscillations and capillary waves. In all these cases we compare DPD results with results available from analytical solutions.

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.

Dissipative particle dynamics simulations of polymer chains: scaling laws and shearing response compared to DNA experiments

Dissipative particle dynamics simulations of several bead-spring representations of polymer chains in dilute solution are used to demonstrate the correct static scaling laws for the radius of gyration. Shear flow results for the wormlike chain simulating single DNA molecules compare well with average extensions from experiments, irrespective of the number of beads. However, coarse graining with more than a few beads degrades the agreement of the autocorrelation of the extension.

A dissipative particle dynamics description of liquid-crystalline phases. I. Methodology and applications

Simulations of nematic and smectic mesophases based on a dissipative particle dynamics approach are discussed. Mesogenic units are built in the form of standard semirigid bead-spring chains. It is shown that nematic phases can be formed for chains containing at least eight beads, provided that the conservative soft-repulsive potential between nonconnected beads is sufficiently strong. Smectic phases are observed only by modifying the repulsive interaction between the main-chain and terminal beads. The simulations indicate that the smectic-nematic and smectic-isotropic phase transitions take place through the buckling of the smectic layering in the system.

Model system for classical fluids out of equilibrium

A model system for classical fluids out of equilibrium, referred to as a dissipative particles dynamics (DPD) solid, is studied by analytical and simulation methods. The time evolution of a DPD particle is described by a fluctuating heat equation. This DPD solid with transport based on collisional transfer (high-density mechanism) is complementary to the Lorentz gas with only kinetic transport (low-density mechanism). Combination of both models covers the qualitative behavior of transport properties of classical fluids over the full-density range. The heat diffusivity is calculated using a mean-field theory, leading to a linear-density dependence of this transport coefficient, which is exact at high densities. Subleading density corrections are obtained as well. At lower densities the model has a conductivity threshold below which heat conduction is absent. The observed threshold is explained in terms of percolation diffusion on a random proximity network. The geometrical structure of this network is the same as in continuum percolation of completely overlapping spheres, but the dynamics on this network differs from continuum percolation diffusion. Furthermore, the kinetic theory for DPD is extended to the generalized hydrodynamic regime, where the wave-number-dependent decay rates of the Fourier modes of the energy and temperature fields are calculated.