Polymer size in dilute solutions in the good-solvent regime

We determine the density expansion of the radius of gyration, of the hydrodynamic radius, and of the end-to-end distance for a monodisperse polymer solution in good-solvent conditions. We consider the scaling limit (large degree of polymerization), including the leading scaling corrections. Using the expected large-concentration behavior, we extrapolate these low-density expansions outside the dilute regime, obtaining a prediction for the radii for any concentration in the semidilute region. For the radius of gyration, comparison with field-theoretical predictions shows that the relative error should be at most 5% in the limit of very large polymer concentrations.     

Equilibrium and dynamical properties of gaussian stiff chain molecules

We present a novel analytically tractable model for stiff chain molecules. The equilibrium distribution function of the chain is derived using the maximum-entropy principle. For that purpose, we first formulate a discrete chain model, where the connections of the points and the restriction on bending are taken into account via constraints. We then perform the limit to a continuous chain and show that the mean-square end-to-end distance and the radius of gyration of the continuous chain are identical with the same quantities of the Kratky-Porod wormlike chain. The dynamics of our chain is investigated in dilute solution without hydrodynamic interactions. The linear dynamical equation is solved by a normal mode analysis. We discuss the dependence of the relaxation times on the single parameter of the model, the persistence length. For small persistence lengths we obtain the well known relaxation times of the Rouse model. In the stiff-chain limit, we find the pure bending relaxation times and, in addition, the rotational relaxation time.     

Estimation and analysis of the rheological properties of a perfluoropolyether through molecular dynamics simulation

Equilibrium and non-equilibrium molecular dynamics simulations of a perfluoropolyether C₈F₁₈O₄ are reported using an atomistic interaction potential. The bulk rheological properties of the perfluoropolyether are investigated through molecular dynamics simulations as a function of both temperature and shear rate. The effect of molecular structure on viscosity is explored in detail. The rotational relaxation time is reported as a function of temperature. Structural properties, including the mean-square end-to-end chain length, the mean-square radius of gyration of chains, and the distribution functions of bond lengths, bond angles, and bond torsional angles are collected and analyzed as functions of shear rate. After an initial plateau, both mean-square end-to-end chain length and mean-square radius of gyration decrease monotonically with increasing shear rate. The behaviors of the rheological and structural properties are explained through an analysis of the individual contributions due to bond stretching, bond bending, and bond torsion, as well as both intramolecular and intermolecular non-bonded interactions. A further analysis is possible through a meticulous breakdown of each contribution into a specific type of mode; e.g., the total bond stretching is comprised of CC, CO, and CF bond stretching terms. In this way, one can relate the shear viscosity to the specific chemical structure of C₈F₁₈O₄.     

Structure of a semidilute polymer solution under steady shear

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.     

高分子/棒状纳米粒子复合物的分子动力学模拟

采用非平衡态分子动力学模拟研究了剪切场下棒状纳米粒子对高分子基体的结构、 动力学和流变性质的影响. 通过比较多种体积分数(0.8%~10%)的纳米复合物及纯熔体的模拟结果发现, 随着纳米粒子的增加, 高分子链的扩散和松弛逐渐受到抑制, 而链尺寸几乎保持不变. 从Weissenberg number(W_i)角度看, 在剪切流场下, 高分子链的结构性质(如归一化的均方回转半径、 回转张量和取向抑制参数)几乎与纳米粒子的体积分数无关, 而高分子链的Tumbling运动受到抑制. 研究还发现, 纳米复合物与纯熔体的剪切黏度曲线趋势基本一致, 即W_i=1将曲线分为平台区和剪切变稀区. 纳米棒的加入仅定量地改变了流体的剪切黏度.     

Transient electric birefringence of wormlike macromolecules in electric fields of arbitrary strength: a computer simulation study

We have studied the birefringence decay of linear models of macromolecules for two different types of flexibility, the broken-rod chain and the wormlike chain, using a computer simulation of a transient electric birefringence experiment. We have paid particular attention to the influence of the intensity of the orienting field, including two orienting mechanisms, the induced dipole, and the permanent dipole. We have compared wormlike and broken-rod models of the same radius of gyration, finding that they present a different decay curve under the influence of the same intensity of the field. We have seen that these differences are due to the faster relaxation times (smaller in the wormlike chain model) and amplitudes, because, regardless of the type of flexibility, the overall size of a molecule (measured by the radius of gyration) essentially determines the longest relaxation time. We have also analyzed how the relaxation process is affected by the degree of flexibility, the orientation mechanisms, and the intensity of the field. Studying a different aspect, we have paid attention to the deformation of a molecule in a transient electric birefringence experiment as a source of information. In this work we have developed equations to characterize this deformation in terms of one of the components of the gyration tensor, if a dynamic light scattering experiment under the influence of an electric field could be performed. To develop this work we have simulated the Brownian dynamics of the different models, relaxing after the removal of an orienting external electric field of arbitrary strength. A comparison with other methods such a the rigid body treatment or the correlation analysis of Brownian trajectories has also been included. We have seen that differences between the two Brownian dynamics methods are small and that the rigid-body treatment is only an acceptable approximation to obtain the longest relaxation time.     

Properties of semidilute polymer solutions: Investigation of an optically labeled three-component system

A three-component system containing a polymer (2), a good solvent (1) for that polymer, and a second polymer (3) that is compatible with component (2) and isorefractive with the solvent (1) has been studied by static and dynamic light-scattering methods. In concentrated toluene (1) solutions of poly(vinyl methyl ether) (3), where appreciable chain overlap occurs and excluded-volume effects are reduced, polystyrene (2) may be studied in the dilute-solution limit. Consequently, these light-scattering measurements provide an explicit measure of both thermodynamic and hydrodynamic changes that occur as the total polymer concentration is increased from dilute to concentrated solution. Precise numerical coefficients, correct scaling exponents, the radius of gyration, and the effective hydrodynamic radius can be measured directly along with the observation of long-wave single-chain reptation motions and short-range cooperative motions in semidilute and concentrated solutions.     

On a quantity describing the degree of chain entanglement in linear polymer systems

In the present paper we define a quantity which describes how strong a polymer system is entangled. In MD computer simulations we apply this definition to samples of polymer melts which were generated with a specific large-scale structure, as characterized by their radius of gyration, end-to-end distance and the “degree” of mutual entanglement of the chains. The quantities mentioned above are monitored over the relaxation of the samples towards equilibrium.     

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains

Molecular-dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model, which includes excluded volume and backbone connectivity of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and nonequilibrium molecular-dynamics simulations at constant temperature and volume using the dissipative particle dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The obtained boundary conditions and slip length show a rich behavior as a function of grafting density and shear velocity.     

Shear thinning in dilute polymer solutions

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.     

The mechanism of the self-assembly of associating DNA molecules under shear flow: Brownian dynamics simulation

A shear flow induces the assembly of DNAs with the sticky spots. In order to strictly interpret the mechanism of shear-induced DNA assembly, Brownian dynamics simulations with the bead-spring model were carried out for these molecules at various ranges of the Weissenberg numbers (We). We calculate a formation time and analyze the radial distribution function of end beads and the probability distribution of fractional extension at the formation time to understand the mechanism of shear-induced assembly. At low Weissenberg number the formation time, which is defined as an elapsed time until a multimer forms for the first time, decreases rapidly, reaching a plateau at We = 1000. A shear flow changes the radial distribution of end beads, which is almost the same regardless of the Weissenberg number. A shear flow deforms and stretches the molecules and generates different distributions between end beads with a stickly spot. The fractional extension progresses rapidly in shear flow from a Gaussian-like distribution to a uniform distribution. The progress of the distribution of fractional extension increases the possibility of meeting of end beads. In shear flow, the inducement of the assembly mainly results from the progress of the probability distribution of fractional extension. We also calculate properties such as the radius of gyration, stretch, and so on. As the Weissenberg number increases, the radius of gyration at the formation time also increases rapidly, reaching a plateau at We = 1000.     

Mesoscale Simulation for Polymer Migration in Confined Uniform Shear Flow

The structure and dynamics of confined single polymer chain in a dilute solution, either in equilibrium or at different shear rates in the uniform shear flow fields, were investigated by means of dissipative particle dynamics simulations. The no-slip boundary condition without density fluctuation near the wall was taken into account to mimic the environment of a nanochannel. The dependences of the radius of gyration, especially in three different directions, and the density profile of the chain mass center ...     

Structural and dynamical properties for confined polymers undergoing planar Poiseuille flow

The authors present the results from nonequilibrium molecular dynamics simulations for the structural and dynamical properties of highly confined linear polymer fluids undergoing planar Poiseuille flow. They study systems confined within pores of several atomic diameters in width and investigate the dependence of the density profiles, the mean squared radius of gyration, the mean squared end-to-end distance, streaming velocity, strain rate, shear stress, and streaming angular velocity as functions of average fluid density and chain length. Their simulation results show that, sufficiently far from the walls, the radius of gyration for molecules under shear in the middle of the pore follows the power law Rg=ANbnu, where Nb is the number of bonds and the exponent has a value of 0.5 which resembles the value for a homogeneous equilibrium fluid. Under the conditions simulated, the authors find the onset of flat velocity profiles but with very little wall slippage. These flat profiles are most likely due to the restricted layering of the fluid into just one or two molecular layers for narrow pore widths compared to chain length, rather than typical plug-flow conditions. The angular velocity is shown to be proportional to half the strain rate in the pore interior when the chain length is sufficiently small compared to the pore width, consistent with the behavior for homogeneous fluids in the linear regime.     

Chitosan and its derivatives in extensional and shear flows

Allylchitosan and propylchitosan with different degrees of substitution were prepared on the basis of chitosan from shrimp chitin. The dynamics of semidilute electrolytic polymer solutions of chitosan derivatives in acetic acid was studied by measuring birefringence in extensional and shear flows and by means of viscometry. The optical shear coefficient and critical velocity gradients corresponding to the loss of stability of the macromolecular coil in extensional flow were found. The chain relaxation times depending on the polyelectrolyte concentration and ionic strength of solution were determined.     

The dynamics of single chains within a model polymer melt

Discontinuous molecular dynamics simulations are performed on a system containing 32 hard chains of length 192 at a volume fraction of phi = 0.45 to explore the idea that localized entanglements have a significant effect on the dynamics of the individual chains within an entangled polymer melt. Anomalous behavior can still be observed when studying the dynamics of the individual chains, although increased time averaging causes the anomalous relaxation-memory-release behavior that was observed previously in the system to smooth out. First, the individual chain mean squared displacements and apparent diffusion coefficients are calculated, and a wide distribution of diffusive behavior is found. Although the apparent diffusion coefficient curve averaged over all chains displays the predicted long-time diffusive behavior, the curves for the individual chains differ both qualitatively and quantitatively. They display superdiffusive, diffusive, and subdiffusive behavior, with the largest percentage of chains exhibiting superdiffusive behavior and the smallest percentage exhibiting the predicted diffusive behavior. Next, the individual chain end-to-end vector autocorrelation functions and relaxation times are determined, and a wide distribution of stress relaxation behavior is found. The times when the end-to-end vector autocorrelation functions relax completely span almost an order of magnitude in reduced time. For some chains, the end-to-end vector autocorrelation function relaxes smoothly toward zero similar to the system average; however, for other chains the relaxation is slowed greatly, indicating the presence of additional entanglements. Almost half of the chains exhibit the anomalous behavior in the end-to-end vector autocorrelation function. Finally, the dynamic properties are displayed for a single chain exhibiting anomalous relaxation-memory-release behavior, supporting the idea that the relaxation-memory-release behavior is a single-chain property.     

Interfacial friction between semiflexible polymers and crystalline surfaces

The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with adjustable intrinsic stiffness. The structure and relaxation dynamics of polymer chains near interfaces are quantified by the radius of gyration and decay of the time autocorrelation function of the first normal mode. We found that the friction coefficient at small slip velocities exhibits a distinct maximum which appears due to shear-induced alignment of semiflexible chain segments in contact with solid walls. At large slip velocities, the friction coefficient is independent of the chain stiffness. The data for the friction coefficient and shear viscosity are used to elucidate main trends in the nonlinear shear rate dependence of the slip length. The influence of chain stiffness on the relationship between the friction coefficient and the structure factor in the first fluid layer is discussed.     

Dynamic light scattering in sols of a poly(N-vinylcaprolactam) and polyacrylamide mixture

The properties of semidilute solutions of a mixture of polyacrylamide and thermoresponsive polyvinylcaprolactam are studied via dynamic light scattering. It is found that the relaxation time (correlation length) distribution contains several modes. The obtained experimental data are interpreted in terms of the theory describing the dynamics of semidilute and concentrated solutions with allowance for viscoelastic interactions. The investigation of mode dispersion (the dependence of relaxation time on the wave vector of scattering) shows that the fastest and slowest modes are of the diffusion type. The fast mode is the mode of collective diffusion; it may be attributed to the fluctuation motion of polymer units inside blobs. The slowest mode corresponds to the diffusion motion of macromolecule clusters. The rate of relaxation of medium modes nonlinearly depends on the squared wave vector, and these modes are apparently viscoelastic.     

Noncontinuum effects on the mobility of nanoparticles in unentangled polymer solutions

The results for the diffusivity of nanoparticles in unentangled semidilute polymer solutions obtained using coarse‐grained simulations are presented. The results indicate that for particle sizes smaller than the polymer radius of gyration, the nanoparticle diffusivities deviate from Stokes–Einstein predictions and depend explicitly on the polymer radius of gyration and the polymer solution correlation lengths. Scaling ideas proposed are invoked for rationalizing such noncontinuum effects and demonstrate that the simulation results could be collapsed onto a single universal function of the depletion thickness, the polymer radius of gyration, and the particle radius. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2145–2150.     

Evidence for the time-temperature superposition principle from Monte-Carlo simulations of the glass transition in two-dimensional polymer melts

The bond fluctuation model on a square lattice with a bond-length dependent potential exhibits in simulations of slow cooling a kinetic glass transition where the system falls out of equilibrium. Extending previous work, the relaxation functions of gyration radius and end-to-end distance, and the bond autocorrelation function of the polymers are presented and related to the time-dependent displacements of inner monomeric units and center of gravity of the whole chains, respectively. Over a wide temperature range the data can be collapsed on master curves satisfying the time-temperature superposition principle for Rouse dynamics.     

Polymer deformation in various flows

Using a Langevin-like approach, the deformation of a polymer, modelled as a bead-spring chain, is calculated in simple shear, elongational and Kramers potential flow. Analytic expressions for the mean-square end-to-end distance, radius of gyration, segment-segment distance, static structure factor up to O(q⁴) and the intrinsic elongational viscosity are given. Near equilibrium, preaveraged hydrodynamic interaction is taken into account.