Anomalous nanoparticle diffusion in polymer solutions and melts: a mode-coupling theory study

Mode-coupling theory is employed to study diffusion of nanoparticles in polymer melts and solutions. Theoretical results are directly compared with molecular dynamics simulation data for a similar model. The theory correctly reproduces the effects of the nanoparticle size, mass, particle-polymer interaction strength, and polymer chain length on the nanoparticle diffusion coefficient. In accord with earlier experimental, simulation, and theoretical work, it is found that when the polymer radius of gyration exceeds the nanoparticle radius, the Stokes-Einstein relation underestimates the particle diffusion coefficient by as much as an order of magnitude. Within the mode-coupling theory framework, a microscopic interpretation of this phenomenon is given, whereby the total diffusion coefficient is decomposed into microscopic and hydrodynamic contributions, with the former dominant in the small particle limit, and the latter dominant in the large particle limit. This interpretation is in agreement with previous mode-coupling theory studies of anomalous diffusion of solutes in simple dense fluids.     

Conformation and diffusion behavior of ring polymers in solution: a comparison between molecular dynamics, multiparticle collision dynamics, and lattice Boltzmann simulations

We have studied the effect of chain topology on the structural properties and diffusion of polymers in a dilute solution in a good solvent. Specifically, we have used three different simulation techniques to compare the chain size and diffusion coefficient of linear and ring polymers in solution. The polymer chain is modeled using a bead-spring representation. The solvent is modeled using three different techniques: molecular dynamics (MD) simulations with a particulate solvent in which hydrodynamic interactions are accounted through the intermolecular interactions, multiparticle collision dynamics (MPCD) with a point particle solvent which has stochastic interactions with the polymer, and the lattice Boltzmann method in which the polymer chains are coupled to the lattice fluid through friction. Our results show that the three methods give quantitatively similar results for the effect of chain topology on the conformation and diffusion behavior of the polymer chain in a good solvent. The ratio of diffusivities of ring and linear polymers is observed to be close to that predicted by perturbation calculations based on the Kirkwood hydrodynamic theory.     

Diffusion of Nanoparticles in Semidilute Polymer Solutions: A Multiparticle Collision Dynamics Study

The diffusion of nanoparticles immersed in semidilute polymer solutions is investigated by a hybrid mesoscopic multiparticle collision dynamics method. Effects of polymer concentration and hydrodynamic interactions among polymer monomers are focused. Extensive simulations show that the dependence of diffusion coefficient D on the polymer concentration c agrees with Phillies equation D-exp (-αc^δ) with a scaling exponent δ≈0.97 which coincides with the experimental one in literature. For increasing nanoparticle size, the scaling prefactor α increases monotonically while the scaling exponent always keeps fixed. Moreover, we also study the diffusion of nanoparticle without hydrodynamic interactions and find that mobility of the nanoparticle slows down, and the scaling exponent is obviously different from the one in experiments, implying that hydrodynamic interactions play a crucial role in the diffusion of a nanoparticle in semidilute polymer solutions.     

The influence of the polymer chain stiffness on tracer diffusion in polymeric matrices

The diffusion of penetrants in polymers is of technological importance in many areas including chromatography and fuel cell membranes. In this work, the effect of chain conformations on tracer diffusion is studied using molecular simulations and a percolation theory. The polymeric matrix is composed of tangent hard sphere chains that are fixed in space; conformations are changed by tuning the stiffness of the chains. The tracer diffusion coefficient is relatively insensitive to the chain stiffness when polymer chains are frozen as in polymer glasses with the local chain dynamics switched off. An analysis of the matrix using percolation theory shows that the polymer volume fraction at the free volume percolation threshold is also relatively insensitive to the chain stiffness, consistent with the diffusion results. This is surprising because the site‐site intermolecular pair correlation functions in the matrix are quite sensitive to the chain stiffness. In contrast, the tracer diffusion coefficient in a melt of mobile chains decreases significantly as the chain stiffness is increased. We conclude that tracer diffusion is only weakly correlated with the chain conformations and local chain dynamics plays an important role. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

高分子/单链高分子纳米粒子复合体系中的界面性质

高分子与纳米粒子复合是改善高分子材料性能的有效途径.近20年来关于高分子/纳米粒子复合物的研究引起了学术界广泛的兴趣.然而由于此类体系中的影响因素复杂,虽然学者们在相关材料性能的研究方面取得了重要进展,但是相关理论的发展却相对滞后,其中一个重要原因是实验上表征手段的缺失,导致对体系中纳米粒子与本体高分子链相互作用规律的认识(尤其是两者界面性质的认识)不够.本文总结和阐述了我们近几年利用分子动力学模拟技术研究高分子/单链高分子纳米粒子复合体系的主要结果,并围绕此类复合体系中的界面结构及动力学性质,讨论并总结了纳米粒子对本体高分子链的作用范围及影响规律,指出单链纳米粒子对熔体链的作用范围与纳米粒子的自身尺寸相当,而与熔体高分子链的分子量没有直接的关系.该结论将为纳米复合体系高分子理论的发展提供重要参考.     

A theoretical study for nanoparticle partitioning in the lamellae of diblock copolymers

Morphology control is important for practical applications of composite materials that consist of functional polymers and nanoparticles. Toward that end, block copolymers provide useful templates to arrange nanoparticles in the scaffold of self-organized polymer microdomains. This paper reports theoretical predictions for the distribution of nanoparticles in the lamellar structures of symmetric diblock copolymers on the basis of a polymer density functional theory (DFT) and the potential distribution theorem (PDT). The DFT predicts periodic spacing of lamellar structures in good agreement with molecular dynamics simulations. With the polymer structure from DFT as the input, the PDT is used to examine the effects of particle size, surface energy, polymer chain length, and compressibility on the distribution of nanoparticles in the limit of low particle density. It is found that the nanoparticle distribution depends not only on the particle size and surface energy but also on the local structure of the microdomain interface, polymer chain length, and compressibility. The theoretical predictions are compared well with experiments and simulations.     

布朗扩散系数对胶体分形粒子簇扩散控制聚集动力学影响的Monte Carlo模拟

使用表征粒子簇结构的几何形状因子,通过对扩散控制聚集过程的模拟,从微观或介观层次研究了粒子簇结构对粒子簇增长速率和速率常数的影响规律,并与实验结果进行了对比分析.     

The Soret effect in dilute polymer solutions: influence of chain length, chain stiffness, and solvent quality

Thermal diffusion in dilute polymer solutions is studied by reverse nonequilibrium molecular dynamics. The polymers are represented by a generic bead-spring model. The influence of the solvent quality on the Soret coefficient is investigated. At constant temperature and monomer fraction, a better solvent quality causes a higher affinity for the polymer to the cold region. This may even go to thermal-diffusion-induced phase separation. The sign of the Soret coefficient changes in a symmetric nonideal binary Lennard-Jones solution when the solvent quality switches from good to poor. The known independence of the thermal diffusion coefficients of the molecular weight is reproduced for three groups of polymers with different chain stiffnesses. The thermal diffusion coefficients reach constant values at chain lengths of around two to three times the persistence length. Moreover, rigid polymers have higher Soret coefficients and thermal diffusion coefficients than more flexible polymers.     

Diffusion of small molecules in glassy polymers

Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO₂ in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO₂ pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2397–2408, 1997     

Diffusion as a probe to assess stretching-induced morphological changes in polyurethane

An analysis of the diffusion of toluene through polyurethane based on bis (p-cyclohexyl diisocyanate), poly(tetramethylene glycol) 1000, and 1,4-butane diol, subjected to varied degrees of elongation by stretching, is presented. The diffusion coefficient is increased by 60% in polymers drawn to 200% and above. Beyond 400% elongation, the diffusion coefficient attained a constant value. Associated changes are observed in the wide-angle x-ray diffraction pattern. These diffusion and x-ray changes are correlated with restructuring of the polymer induced by stretching. © 1993 John Wiley & Sons, Inc.     

Electrostatic relaxation and hydrodynamic interactions for self-diffusion of ions in electrolyte solutions

The concentration dependence of self-diffusion of ions in solutions at large concentrations has remained an interesting yet unsolved problem. Here we develop a self-consistent microscopic approach based on the ideas of mode-coupling theory. It allows us to calculate both contributions which influence the friction of a moving ion: the ion atmosphere relaxation and hydrodynamic interactions. The resulting theory provides an excellent agreement with known experimental results over a wide concentration range. Interestingly, the mode-coupling self-consistent calculation of friction reveal a nonlinear coupling between the hydrodynamic interactions and the ion atmosphere relaxation which enhances ion diffusion by reducing friction, particularly at intermediate ion concentrations. This rather striking result has its origin in the similar time scales of the relaxation of the ion atmosphere relaxation and the hydrodynamic term, which are essentially given by the Debye relaxation time. The results are also in agreement with computer simulations, with and without hydrodynamic interactions.     

Diffusion Spectrum of Polymer Melt Measured by Varying Magnetic Field Gradient Pulse Width in PGSE NMR

The translational motion of polymers is a complex process and has a big impact on polymer structure and chemical reactivity. The process can be described by the segment velocity autocorrelation function or its diffusion spectrum, which exhibit several characteristic features depending on the observational time scale—from the Brownian delta function on a large time scale, to complex details in a very short range. Several stepwise, more-complex models of translational dynamics thus exist—from the Rouse regime over reptation motion to a combination of reptation and tube-Rouse motion. Accordingly, different methods of measurement are applicable, from neutron scattering for very short times to optical methods for very long times. In the intermediate regime, nuclear magnetic resonance (NMR) is applicable—for microseconds, relaxometry, and for milliseconds, diffusometry. We used a variation of the established diffusometric method of pulsed gradient spin-echo NMR to measure the diffusion spectrum of a linear polyethylene melt by varying the gradient pulse width. We were able to determine the characteristic relaxation time of the first mode of the tube-Rouse motion. This result is a deviation from a Rouse model of polymer chain displacement at the crossover from a square-root to linear time dependence, indicating a new long-term diffusion regime in which the dynamics of the tube are also described by the Rouse model.     

Self‐diffusion coefficient of ring polymers in semidilute solution

In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self‐diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008     

DNA diffusion in aqueous solution in presence of suspended particles

Although nanoparticles, which are comparable in size to polymer chains, are widely used as fillers to polymer matrices for developing functional and high performance materials, the dynamics of polymers constrained between solid particles has not been well elucidated. In this study, dynamics of individual polymer under such condition was investigated with fluorescent microscopy using DNA solutions as model systems. For individual T4 and λ DNA molecules in aqueous suspensions of spherical polystyrene particles with diameter of 1 μm, it was found that (i) the radius of gyration of DNA is independent of the particle volume fraction, ?_p, (ii) DNA diffusion is not sensitive to ?_p up to a certain critical ?_p where the average distance between particle surfaces is close to DNA size, and (iii) the DNA diffusion becomes slower at higher ?_p. The diffusion coefficient of DNA was larger, by a factor of 2, in the suspensions at intermediate ?_p than in the corresponding confined geometry (channel/slit between fixed walls), whereas this difference asymptotically vanished with increasing ?_p. This result suggested that the DNA diffusion in the suspensions with intermediate ?_p is accelerated by the particle motion. In fact, the diffusion coefficient measured for DNA in the suspensions was semiquantitatively described by the Rouse constraint‐release model considering the matrix effect on the probe chain diffusion. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1103–1111, 2009     

Holographic grating relaxation studies of probe diffusion in amorphous polymers

Probe diffusion of camphorquinone, thymoquinone, and diacetyl in polymers was studied by the laser-induced holographic grating relaxation (HGR) technique in polymers. The effects of changing the probe size and various parameters of the polymer, such as the molecular weight, chain conformation, and the glass transition temperature, on the probe diffusion coefficient have been investigated. Furthermore, effects of cross-linking and plasticizing the chains of the polymer host on the probe diffusion coefficient were also studied. Temperature-dependent studies show that except for the very low molecular weight poly(methyl methacrylate), all probe diffusion coefficient data above the glass transition temperature fit well to the WLF equation. ©1995 John Wiley & Sons, Inc.     

Polymer grafted nanoparticles: Effect of chemical and physical heterogeneity in polymer grafts on particle assembly and dispersion

Macroscopic properties of polymer nanocomposites depend on the microscopic composite morphology of the constituent nanoparticles and polymer matrix. One way to control the spatial arrangement of the nanoparticles in the polymer matrix is by grafting the nanoparticle surfaces with polymers that can tune the effective interparticle interactions in the polymer matrix. A fundamental understanding of how graft and matrix polymer chemistries and molecular weight, grafting density, and nanoparticle size, and chemistry affect interparticle interactions is needed to design the appropriate polymer ligands to achieve the target morphology. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level interactions to the morphology. In this feature article, we present our recent theory and simulation studies of polymer grafted nanoparticles with chemical and physical heterogeneity in grafts to calculate the effective interactions and morphology as a function of chemistry, molecular weights, grafting densities, and so forth. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Theory of nanoparticle diffusion in unentangled and entangled polymer melts

We propose a statistical dynamical theory for the violation of the hydrodynamic Stokes-Einstein (SE) diffusion law for a spherical nanoparticle in entangled and unentangled polymer melts based on a combination of mode coupling, Brownian motion, and polymer physics ideas. The non-hydrodynamic friction coefficient is related to microscopic equilibrium structure and the length-scale-dependent polymer melt collective density fluctuation relaxation time. When local packing correlations are neglected, analytic scaling laws (with numerical prefactors) in various regimes are derived for the non-hydrodynamic diffusivity as a function of particle size, polymer radius-of-gyration, tube diameter, degree of entanglement, melt density, and temperature. Entanglement effects are the origin of large SE violations (orders of magnitude mobility enhancement) which smoothly increase as the ratio of particle radius to tube diameter decreases. Various crossover conditions for the recovery of the SE law are derived, which are qualitatively distinct for unentangled and entangled melts. The dynamical influence of packing correlations due to both repulsive and interfacial attractive forces is investigated. A central finding is that melt packing fraction, temperature, and interfacial attraction strength all influence the SE violation in qualitatively different directions depending on whether the polymers are entangled or not. Entangled systems exhibit seemingly anomalous trends as a function of these variables as a consequence of the non-diffusive nature of collective density fluctuation relaxation and the different response of polymer-particle structural correlations to adsorption on the mesoscopic entanglement length scale. The theory is in surprisingly good agreement with recent melt experiments, and new parametric studies are suggested.     

The properties of a single polymer chain in solvent confined in a slit: A molecular dynamics simulation

A single polymer chain in solvent confined in a slit formed by two parallel plates is studied by using molecular dynamics simulation method. The square radii of gyration and diffusion behaviors of polymers are greatly affected by the distance between the two plates, but they do not follow the same way. The chain size decays drastically with increasing h (h is the distance between two plates), until a basin occurs, and a universal h/〈R _g〉₀ dependence for polymer chains with different degrees of polymerization can be obtained. While, for the chain’s diffusion coefficient, it decays monotonously and there is no such basin-like behavior. Furthermore, we studied the radial distribution function of confined polymer chains to explain the reason why there is a difference for the decay behaviors between dynamic properties and static properties. Besides, we also give the degree of confinement dependence of the static scaling exponent for a single polymer chain. Our work provides an efficient way to estimate the dynamics and static properties of confined polymer chains, and also helps us to understand the behavior of polymer chains under confinement.     

Numerical simulation on polymer translocation into crowded environment with nanoparticles

The effects of crowded environment with nano particles are studied for polymer translocation through a small pore. The translocation time τ is simulated by Fokker-Planck equation at different free energy landscapes F and diffusion coefficients of polymer D. The free energy is calculated using the Rosenbluth-Rosenbluth method, and the diffusion coefficient is followed the relation \(D \sim \frac {1}{N} e^{-\triangle F}\). We find that the free energy is dependent on polymer-nanoparticle interaction, size of the nanoparticle, and position of the nanoparticle. The attractive nanoparticles at the trans side can provide a driving force to polymer by lowering the free energy, but the exclusive effect of nanoparticle can raise the free energy of polymer. There exists an optimum interaction that τ is roughly independent on the size and position of nanoparticles. It is found that these effects are related to the conformational change of polymer chain in crowded environment.