Collective dynamics of polymer solutions

Conformation Dynamics of Single Polymer Strands in Solution

Conformational changes in macromolecules significantly affect their functions and assembly into high-level structures. Despite advances in theoretical and experimental studies, investigations into the intrinsic conformational variations and dynamic motions of single macromolecules remain challenging. Here, liquid-phase transmission electron microscopy enables the real-time tracking of single-chain polymers. Imaging linear polymers, synthetically dendronized with conjugated aromatic groups, in organic solvent confined within graphene liquid cells, directly exhibits chain-resolved conformational dynamics of individual semiflexible polymers. These experimental and theoretical analyses reveal that the dynamic conformational transitions of the single-chain polymer originate from the degree of intrachain interactions. In situ observations also show that such dynamics of the single-chain polymer are significantly affected by environmental factors, including surfaces and interfaces.

Dynamical self-consistent field theory captures multi-scale physics during spinodal decomposition in a symmetric binary homopolymer blend

We study the spinodal decomposition in a symmetric, binary homopolymer blend using our recently developed dynamical self-consistent field theory. By taking the extremal solution of a dynamical functional integral, the theory reduces the interacting, multi-chain dynamics to a Smoluchowski equation describing the statistical dynamics of a single, unentangled chain in a self-consistent, time-dependent, mean force-field. We numerically solve this equation by evaluating averages over a large ensemble of replica chains, each one of which obeys single-chain Langevin dynamics, subject to the mean field. Following a quench from the disordered state, an early time spinodal instability in the blend composition develops, before even one Rouse time elapses. The dominant, unstable, growing wavelength is on the order of the coil size. The blend then enters a late-time, t, scaling regime with a growing domain size that follows the expected Lifshitz-Slyozov-Wagner t^1/3 power law, a characteristic of a diffusion-driven coarsening process. These results provide a satisfying test of this new method, which correctly captures both the early and late time physics in the blend. Our simulation spans five orders-of-magnitude in time as the domains coarsen to 20 times the coil size, while remaining faithful to the dynamics of the microscopic chain model.

Active force maintains the stability of a contractile ring

We investigate a system of sufficiently dense polar actin filaments considered rigid and cross-linked by dimer myosin II protein within the contractile ring. The Langevin dynamics of this system is cast in a functional integral formalism and then transformed into density variables. Using the dynamical Random Phase Approximation (RPA) along with the a one-dimensional Langevin dynamics simulation (LDS), we investigate the structural integrity of the actin bundle network. The active force and the networking force reveal a non-trivial diffusive behaviour of the filaments within the ring. We conclude on when the active and networking forces lead to the contractile ring breaking down. The non-equilibrium active force is predominantly responsible for the prevention of the gaps in the ring.

Solvent vapor annealing in block copolymer nanocomposite films: a dynamic mean field approach

Polymer nanocomposites are an important class of materials due to the nanoparticles' ability to impart functionality not commonly found in a polymer matrix, such as electrical conductivity or tunable optical properties. While the equilibrium properties of polymer nanocomposites can be treated using numerous theoretical and simulation approaches, in experiments the effects of processing and kinetic traps are significant and thus critical for understanding the structure and the functionality of polymer nanocomposites. However, simulation methods that can efficiently predict kinetically trapped and metastable structures of polymer nanocomposites are currently not common. This is particularly important in inhomogeneous polymers such as block copolymers, where techniques such as solvent vapor annealing are commonly employed to improve the long-range order. In this work, we introduce a dynamic mean field theory that is capable of predicting the result of processing the structure of polymer nanocomposites, and we demonstrate that our method accurately predicts the equilibrium properties of a model system more efficiently than a particle-based model. We subsequently use our method to predict the structure of block copolymer thin films with grafted nanoparticles after solvent annealing, where we find that the final distribution of the grafted nanoparticles can be controlled by varying the solvent evaporation rate. The extent to which the solvent evaporation rate can affect the final nanoparticle distribution in the film depends on the grafting density and the length of the grafted chains. Furthermore, the effects of the solvent evaporation rate can be anticipated from the equilibrium nanoparticle distribution in the swollen and dry states.

Rheological Study and Molecular Dynamics Simulation of Biopolymer Blend Thermogels of Tunable Strength

The temperature-induced gelation of chitosan/glycerophosphate (Chs/GP) systems through physical interactions has shown great potential for various biomedical applications. In the present work, hydroxyethyl cellulose (HEC) was added to the thermosensitive Chs/GP solution to improve the mechanical strength and gel properties of the incipient Chs/HEC/GP gel in comparison with the Chs/GP hydrogel at body temperature. The physical features of the macromolecular complexes formed by the synergistic interaction between chitosan and hydroxyethyl cellulose in the presence of β-glycerophosphate disodium salt solution have been studied essentially from a rheological point of view. The temperature and time sweep rheological characterizations of the thermogelling systems revealed that the sol-gel transition temperature of the Chs/HEC/GP blends is equal to 37 °C at neutral pH; with increasing HEC content in the solutions, more compact networks with considerably improved gel strength are formed without influencing the gelation time. The formed hydrogel matrix has enough mechanical integrity and adequate strength for using it as injectable in situ forming matrices for biomedical applications. The classical Winter-Chambon (W-C) and Fredrickson-Larson (F-L) theories were applied to determine the gel point. In view of the obtained results, it is shown that the F-L theory can be employed as a robust and less tedious method than the W-C approach to precisely determine the gel point in these systems. At the end, molecular simulation studies were conducted by using ab initio quantum mechanics (QM) calculations carried out on Chs and HEC models, and molecular dynamics (MD) simulations of solvated Chs/HEC blend systems showed the binding behavior of Chs/HEC polymers. Analyses of interaction energy, radial distribution function, and hydrogen bonding from simulation studies strongly supported the experimental results; they all disclosed that hydrogen-bond formation between Chs moieties with regard to HEC chains plays an important role for the stabilization of the complexes.

Mode-coupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations

We quantitatively assess the effect of density fluctuation modes on the dynamics of a tagged polymer in an unentangled melt. To this end, we develop a density-based mode-coupling theory (dMCT) using the Mori-Zwanzig approach and projecting the fluctuating force onto pair-density fluctuation modes. The effect of dynamical density fluctuations on the center-of-mass (c.m.) dynamics is also analyzed based on a perturbative approach and we show that dMCT and perturbation techniques yield identical results. The c.m. velocity autocorrelation function (c.m. VAF) exhibits a slow power law relaxation in the time range between the monomer time t_{1} and the Rouse relaxation time t_{N}. We obtain an analytical expression for the c.m. VAF in terms of molecular parameters. In particular, the c.m. VAF scales as -N^{-1}t^{-5/4} (where N is the number of monomer units per chain) in the relevant time regime. The results are qualitatively accounted for by the dynamical correlation hole effect. The predicted -t^{-5/4} dependence of the c.m. VAF is supported by data of non-momentum-conserving computer simulations. However, the comparison shows that the theory significantly underestimates the amplitude of the effect. This issue is discussed and an alternative approach is addressed in the second part of this series [Farago et al., Phys. Rev. E 85, 051807 (2012), the following paper].

Mode-coupling approach to polymer diffusion in an unentangled melt. II. The effect of viscoelastic hydrodynamic interactions

A mode-coupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [Farago, Meyer, and Semenov, Phys. Rev. Lett. 107, 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the density-based MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the center-of-mass velocity autocorrelation function (c.m. VAF). We show that in most cases the VHI mechanism is dominant; for long chains and prediffusive times it yields a negative tail ∝-N^{-1/2}t^{-3/2} for the c.m. VAF. The case of non-momentum-conserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first -N^{-1}t^{-5/4} (as in the dMCT approach), then -N^{-1/2}t^{-3/2}. Both the amplitude and the duration of the first t^{-5/4} stage crucially depend on the Langevin friction parameter γ. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the c.m. VAF, thus account for the anomalous subdiffusive regime of the c.m. mean square displacement widely observed in numerical and experimental works.

Rotational and translational diffusion of fluorocarbon tracer spheres in semidilute xanthan solutions

We report an experimental study of rotational and translational diffusion and sedimentation of colloidal tracer spheres in semidilute solutions of the nonadsorbing semiflexible polymer xanthan. The tracers are optically anisotropic, permitting depolarized dynamic light scattering measurements without interference from the polymer background. The xanthan solutions behave rheologically like model semidilute polymeric solutions with long-lived entanglements. On the time scale of tracer motion the xanthan solutions are predominantly elastic. The generalized Stokes-Einstein relation describing the polymer solution as a continuous viscous fluid therefore severely overestimates the tracer hindrance. Instead, effective medium theory, describing the polymer solution as a homogeneous Brinkman fluid with a hydrodynamic screening length equal to the concentration-dependent static correlation length, is in excellent agreement with the tracer sedimentation and rotational diffusion coefficients. Rotational diffusion, however, is at the same time in good agreement with a simple model of a rotating sphere in a concentric spherical depletion cavity. Translational diffusion is faster than predicted for a Brinkman fluid, likely due to polymer depletion.

Self-generated disorder and structural glass formation in homopolymer globules

We have investigated the interrelation between spin glasses and structural glasses. Spin glasses in this case are p-spin interaction spin glasses (at p>2) or Potts glasses that contain quenched disorder, whereas the structural glasses are here exemplified by a homopolymeric globule, which can be viewed as a liquid of connected units on a nanoscale. It is argued that the homopolymeric globule problem can be mapped onto a disorder field theoretical model whose effective Hamiltonian resembles the corresponding one for the spin glass model. In this sense the disorder in the globule is self-generated (in contrast to spin glasses) and can be related to competing interactions (virial coefficients of different signs) and the chain connectivity. The work is aimed at giving a quantitative description of this analogy. We have investigated in the mean-field approximation the phase diagram of the homopolymeric globule where the transition line from the liquid to glassy globule is treated in terms of the replica symmetry breaking paradigm. The configurational entropy temperature dependence is also discussed.

Dynamic charge-density correlation function in weakly charged polyampholyte globules

We study solutions of statistically neutral polyampholyte chains containing a large fraction of neutral monomers. It is known that such solutions phase separate at very low concentrations, even if the quality of the solvent with respect to the neutral monomers is good. The precipitate is semidilute if the chains are weakly charged. This paper considers straight theta solvents and good solvents, and we calculate the dynamic charge density correlation function g(k,t) in the precipitate, using the quadratic approximation to the Martin-Siggia-Rose generating functional. It is convenient to express the results in terms of dimensionless space and time variables. Let xi be the blob size, and let tau be the characteristic time scale at the blob level. Define the dimensionless wave vector q=xik, and the dimensionless time s=t/tau. In the regime q<1, corresponding to length scales larger than the blob size, and 1<s<q(-4), corresponding to time scales in between the blob relaxation time and the relaxation time at scale q(-1), we find that the charge density fluctuations relax according to the power law g(q,s) approximately q(2)s(-1/2). This relaxation is qualitatively different from that of a neutral semidilute polymer solution. We expect our results to be valid for wave vectors q>0.1, where entanglements are unimportant.

Screening of hydrodynamic interactions in semidilute polymer solutions: a computer simulation study

We study single-chain motion in semidilute solutions of polymers of length N=1000 with excluded-volume and hydrodynamic interactions by a novel algorithm. The crossover length of the transition from Zimm (short lengths and times) to Rouse dynamics (larger scales) is proportional to the static screening length. The crossover time is the corresponding Zimm time. Our data indicate Zimm behavior at large lengths but short times. There is no hydrodynamic screening until the chains feel constraints, after which they resist the flow: "Incomplete screening" occurs in the time domain.