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Semiflexible polymer rings whose bonds obey both angular and dihedral restrictions [M. Dolgushev and A. Blumen, J. Chem. Phys. 138, 204902 (2013)], are treated under exact closure constraints. This allows us to obtain semianalytic results for their dynamics, based on sets of Langevin equations. The dihedral restrictions clearly manifest themselves in the behavior of the mean-square monomer displacement. The determination of the equilibrium ring conformations shows that the dihedral constraints influence the ring curvature, leading to compact folded structures. The method for imposing such constraints in Gaussian systems is very general and it allows to account for heterogeneous (sitedependent) restrictions. We show it by considering rings in which one site differs from the others. [ABSTRACT FROM AUTHOR]

We study the orientational properties of labeled segments in semiflexible dendrimers making use of the viscoelastic approach of Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)]. We focus on the segmental orientational autocorrelation functions (ACFs), which are fundamental for the frequency-dependent spin-lattice relaxation times T1(ω). We show that semiflexibility leads to an increase of the contribution of large-scale motions to the ACF. This fact influences the position of the maxima of the [1/T1]-functions. Thus, going from outer to inner segments, the maxima shift to lower frequencies. Remarkably, this feature is not obtained in the classical bead-spring model of flexible dendrimers, although many experiments on dendrimers manifest such a behavior. [ABSTRACT FROM AUTHOR]

Here we consider the dynamics of semiflexible polymers subject both to angular and to dihedral constraints. We succeed in obtaining analytically the dynamical matrix of such systems by extending the formalism developed by Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)]. This leads to a set of Langevin equations whose eigenvalues determine many dynamical properties. Exemplarily, we display the mechanical relaxation loss moduli [G″(ω)] as a function of several, distinct sets of microscopic stiffness parameters; it turns out that such differences lead to macroscopically distinct patterns. [ABSTRACT FROM AUTHOR]

We study the dynamics of semiflexible dendritic polymers following the method of Dolgushev and Blumen [J. Chem. Phys. 131, 044905 (2009)]. The scheme allows to formulate in analytical form the corresponding Langevin equations. We determine the eigenvalues by first block-diagonalizing the problem, which allows to treat even very large dendritic objects. A basic ingredient of the procedure is the observation that a set of eigenmodes in the semiflexible case is similar to that chosen by Cai and Chen [Macromolecules 30, 5104 (1997)] for fully flexible dendritic structures. Varying the flexibility of the macromolecules allows us to better understand their mechanical loss moduli G″(ω) based on their eigenvalue spectra. We present the G″(ω) for a series of stiffness parameters and for different functionalities of the branching points. [ABSTRACT FROM AUTHOR]

Based on the success of the maximum entropy principle (MEP) in the study of semiflexible treelike polymers [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], it is of much interest to establish MEP's potential for general semiflexible polymers which contain loops. Here, we embark on this endeavor by considering discrete semiflexible polymer rings in a Rouse-type scheme. Now, for treelike polymers a beads-and-bonds (i.e., a discrete) picture is essential for an easy inclusion of branching points. Moreover, one may envisage (similar to our former work [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)]) to impose for each angle between two bonds a distinct stiffness condition. Working in this way leads already for a polymer ring to a complicated problem. Hence, we follow a reduced variational approach as applied earlier to polymer chains, in which a single Lagrange multiplier is used for each set of identical conditions imposed on topologically equivalent bonds and bonds' orientations. In this way, we obtain for the discrete ring an analytically closed form which involves Chebyshev polynomials. This expression turns out to lead to a series of solutions: Apart from the regular solution, several other solutions appear. One may be tempted to discard the other solutions, since for them the potential energy matrix is not positive definite. A more careful analysis based on topological features suggests, however, that such solutions can be assigned to rings displaying knots. Monte Carlo simulations which take excluded volume interactions into account agree with our interpretation. [ABSTRACT FROM AUTHOR]

We consider polymer structures which are known in the mathematical literature as 'cospectral.' Their graphs have (in spite of the different architectures) exactly the same Laplacian spectra. Now, these spectra determine in Gaussian (Rouse-type) approaches many static as well as dynamical polymer characteristics. Hence, in such approaches for cospectral graphs many mesoscopic quantities are predicted to be indistinguishable. Here we show that the introduction of semiflexibility into the generalized Gaussian structure scheme leads to different spectra and hence to distinct macroscopic patterns. Moreover, particular semiflexible situations allow us to distinguish well between cospectral structures. We confirm our theoretical results through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Based on our recent model for the dynamics of semiflexlible treelike networks [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], we study the dynamical properties of chain polymers and of dendrimers whose junctions display different stiffness degrees (SD). In these polymers the functionality f of the inner junctions is constant, being f=2 for the linear chains and f=3 for the dendrimers. This allows us to focus on the effects caused by the heterogeneities due to different SD. For this we study alternating, diblock, as well as random arrangements of the SD. Each of these cases shows a particular, macroscopically observable behavior, which allows to distinguish between the different microscopic SD arrangements. [ABSTRACT FROM AUTHOR]

We study the dynamics of general treelike networks, which are semiflexible due to restrictions on the orientations of their bonds. For this we extend the generalized Gaussian structure model, in which the dynamics obeys Langevin equations coupled through a dynamical matrix. We succeed in formulating analytically this matrix for arbitrary treelike networks and stiffness coefficients. This allows the straightforward determination of dynamical characteristics relevant to mechanical and dielectric relaxation. We show that our approach also follows from the maximum entropy principle; this principle was previously implemented for linear polymers and we extend it here to arbitrary treelike architectures. [ABSTRACT FROM AUTHOR]

We present a fully atomistic Langevin dynamics approach as a method to simulate biopolymers under external forces. In the harmonic regime, this approach permits the computation of the long-term dynamics using only the eigenvalues and eigenvectors of the Hessian matrix of second derivatives. We apply this scheme to identify polymorphs of model proteins by their mechanical response fingerprint, and we relate the averaged dynamics of proteins to their biological functionality, with the ion channel gramicidin A, a phosphorylase, and neuropeptide Y as examples. In an environment akin to dilute solutions, even small proteins show relaxation times up to 50 ns. Atomically resolved Langevin dynamics computations have been performed for the stretched gramicidin A ion channel. [ABSTRACT FROM AUTHOR]

Starting from exact relations for finite Husimi cacti we determine their complete spectra to very high accuracy. The Husimi cacti are dual structures to the dendrimers but, distinct from these, contain loops. Our solution makes use of a judicious analysis of the normal modes. Although close to those of dendrimers, the spectra of Husimi cacti differ. From the wealth of applications for measurable quantities which depend only on the spectra, we display for Husimi cacti the behavior of the fluorescence depolarization under quasiresonant Förster energy transfer. [ABSTRACT FROM AUTHOR]

We consider end-grafted chains at an adsorbing surface under good solvent conditions using Monte Carlo simulations and scaling arguments. Grafting of chains allows us to fix the surface concentration and to study a wide range of surface concentrations from the undersaturated state of the surface up to the brushlike regime. The average extension of single chains in the direction parallel and perpendicular to the surface is analyzed using scaling arguments for the two-dimensional semidilute surface state according to Bouchaud and Daoud [J. Phys. (Paris) 48, 1991 (1987)]. We find good agreement with the scaling predictions for the scaling in the direction parallel to the surface and for surface concentrations much below the saturation concentration (dense packing of adsorption blobs). Increasing the grafting density we study the saturation effects and the oversaturation of the adsorption layer. In order to account for the effect of excluded volume on the adsorption free energy we introduce a new scaling variable related with the saturation concentration of the adsorption layer (saturation scaling). We show that the decrease of the single chain order parameter (the fraction of adsorbed monomers on the surface) with increasing concentration, being constant in the ideal semidilute surface state, is properly described by saturation scaling only. Furthermore, the simulation results for the chains’ extension from higher surface concentrations up to the oversaturated state support the new scaling approach. The oversaturated state can be understood using a geometrical model which assumes a brushlike layer on top of a saturated adsorption layer. We provide evidence that adsorbed polymer layers are very sensitive to saturation effects, which start to influence the semidilute surface scaling even much below the saturation threshold. [ABSTRACT FROM AUTHOR]

We model coherent exciton transport in dendrimers by continuous-time quantum walks. For dendrimers up to the second generation the coherent transport shows perfect recurrences when the initial excitation starts at the central node. For larger dendrimers, the recurrence ceases to be perfect, a fact which resembles results for discrete quantum carpets. Moreover, depending on the initial excitation site, we find that the coherent transport to certain nodes of the dendrimer has a very low probability. When the initial excitation starts from the central node, the problem can be mapped onto a line which simplifies the computational effort. Furthermore, the long time average of the quantum mechanical transition probabilities between pairs of nodes shows characteristic patterns and allows us to classify the nodes into clusters with identical limiting probabilities. For the (space) average of the quantum mechanical probability to be still or to be again at the initial site, we obtain, based on the Cauchy-Schwarz inequality, a simple lower bound which depends only on the eigenvalue spectrum of the Hamiltonian. [ABSTRACT FROM AUTHOR]

The irreversible adsorption of single chains grafted with one end to the surface is studied using scaling arguments and computer simulations. We introduce a two-phase model, in which the chain is described by an adsorbate portion and a corona portion formed by nonadsorbed monomers. The adsorption process can be viewed as consisting of a main stage, during which monomers join by “zipping” (along their order in the chain) the surface, and a late stage, in which the remaining corona collapses on the surface. Based on our model we derive a scaling relation for the time of adsorption t(M) as a function of the number M of adsorbed monomers; t(M) follows a power law, Mα, with α>1. We find that α is related to the Flory exponent ν by α=1+ν. Using further scaling arguments we derive relations between the overall time of adsorption, the characteristic time of adsorption (given by the crossover time between the main and the last stage of adsorption), and the chain length. To support our analysis we perform Monte Carlo simulations using the bond fluctuation model. In particular, the sequence of adsorption events is very well reproduced by the simulations, and an analysis of the various density profiles supports our theoretical model. Especially the loop formation during adsorption clearly shows that the growth of the adsorbate is dominated by zipping. The simulations are also in almost quantitative agreement with our theoretical scaling analysis, showing that here the assumption of a linear relation between Monte Carlo steps and time is well obeyed. We conclude by also discussing the geometrical shape of the adsorbate. [ABSTRACT FROM AUTHOR]

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time τ of the fluctuations of a free chain in a good solvent grows as τ∼Na, where the coefficient a obeys a=2ν+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state τ⊥, the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; τ⊥ is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by τ∥∼N2ν2+1L-2Δν/ν, where ν2 is the Flory exponent in two dimensions, ν is the Flory exponent in three dimensions, and Δν=ν2-ν. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time. [ABSTRACT FROM AUTHOR]

We present extensive Monte Carlo simulations of tethered chains of length N on adsorbing surfaces, considering the dilute case in good solvents, and analyze our results using scaling arguments. We focus on the mean number M of chain contacts with the adsorbing wall, on the chain’s extension (the radius of gyration) perpendicular and parallel to the adsorbing surface, on the probability distribution of the free end and on the density profile for all monomers. At the critical adsorption strength εc one has Mc∼N[lowercase_phi_synonym], and we find (using the above results) as best candidate [lowercase_phi_synonym] to equal 0.59. However, slight changes in the estimation of εc lead to large deviations in the resulting [lowercase_phi_synonym]; this might be a possible reason for the difference in the [lowercase_phi_synonym] values reported in the literature. We also investigate the dynamical scaling behavior at εc, by focusing on the end-to-end correlation function and on the correlation function of monomers adsorbed at the wall. We find that at εc the dynamic scaling exponent a (which describes the relaxation time of the chain as a function of N) is the same as that of free chains. Furthermore, we find that for tethered chains the modes perpendicular to the surface relax quicker than those parallel to it, which may be seen as a splitting in the relaxation spectrum. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Examines the Monte Carlo simulation of polymer blends in the absence of interactions. Difference of the microphases length with the mean radius of gyration; Calculation of the structure function and different interaction parameters; Comparison of the results to theoretical models.

Studies the block copolymer films between neutral walls using the Monte Carlo method. Film geometry, bulk and surface regions; Perpendicular orientation of lamellae for several box sizes; Preferential stretching of the chains in the direction parallel to the walls.

Studies the computer simulations of asymmetric block copolymers. Use of the lattice bond-fluctuation method; Changes in the A-B interaction parameter; Appearance of Bragg-reflexes in the collective structure factor S(q).

Performs dynamic Monte Carlo simulations on dense symmetric copolymer melts using the bond-fluctuation-algorithm. Model and simulation technique; Collective structure factor; Box-counting; Concentration profiles; Static properties of single chains; Diffusion of center of mass; Relaxation of the end-to-end vector.

We investigate using scaling methods and Monte Carlo simulations random AB-copolymers at the interface between two good solvents. The asymmetry of the interface potential gives rise to an adsorption–desorption transition which shows for infinitely long chains a critical point. For finite chains we analyze the crossover scaling behavior near this critical point. Two new interface exponents, namely the crossover exponent [lowercase_phi_synonym] and the interface order parameter exponent β are proposed. Simulation results obtained using the bond fluctuation model agree well with the scaling predictions. From the simulation data we obtain as best estimates [lowercase_phi_synonym]=1.3±0.1 and β=0.35±0.04. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We investigate the behavior of polymer chains embedded in a lamellar matrix by considering both a regular periodic environment and the effect of disturbances. By using the Green’s function formalism and an attractive Kronig–Penney model, we obtain analytically exact results. For the case of a regular lamellar matrix of period ξ, a long polymer chain is characterized by an effective segment length leff, in analogy to the effective mass of electrons in solids. For potential wells deep enough there appears a gap of forbidden states which separates the low-lying, adsorption band from the higher lying, desorption band. Due to the ground-state dominance, for polymers only the lowest lying states are of physical relevance. Isolated defects of the periodic structure may localize the polymer, in the sense that infinitely long chains are confined inside a region of finite extent L around the defect. For a single defect we find L=1/(εΔξ), where ε is the strength of the periodic potential and Δξ is the deviation from the periodicity. This is also valid for finite chains when their number of segments exceeds the cross-over value NL=2L2/l2eff. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the quantum dynamics of Gaussian wave packets on star graphs whose arms feature each a periodic potential and an external time-dependent field. Assuming that the potentials and the field can be manipulated separately for each arm of the star, we show that it is possible to manipulate the direction of the motion of a Gaussian wave packet through the bifurcation point by a suitable choice of the parameters of the external fields. In doing so, one can achieve a transmission of the wave packet into the desired arm with nearly 70 % while also keeping the shape of the wave packet approximately intact. Since a star graph is the simplest element of many other complex graphs, the obtained results can be considered as the first step to wave packet manipulations on complex networks. [ABSTRACT FROM AUTHOR]

Within the broad class of hyperbranched polymers, highly symmetrical objects (such as dendrimers and Vicsek fractals) are of special theoretical interest. Here we study, using the MARTINI force-field, polyamidoamine Vicsek fractals (PVF) in silico, focusing on their structure and dynamics in dilute solution. Our extensive microsecond-long simulations show that the radius of gyration of PVF scales with the molecular weight as N0.54, behavior rather close to that of stars and considerably distinct from that of dendrimers. The study of the radial density profiles indicates that different parts of the PVF interpenetrate significantly, fact which stresses the soft and sparse character of PVF. These results are also supported by our findings for the rotational autocorrelation functions. [ABSTRACT FROM AUTHOR]

We study the dynamics of continuous-time quantum walks (CTQW) on networks with highly degenerate eigenvalue spectra of the corresponding connectivity matrices. In particular, we consider the two cases of a star graph and of a complete graph, both having one highly degenerate eigenvalue, while displaying different topologies. While the CTQW spreading over the network-in terms of the average probability to return or to stay at an initially excited node-is in both cases very slow, also when compared to the corresponding classical continuous-time random walk (CTRW), we show how the spreading is enhanced by randomly adding bonds to the star graph or removing bonds from the complete graph. Then, the spreading of the excitations may become very fast, even outperforming the corresponding CTRW. Our numerical results suggest that the maximal spreading is reached halfway between the star graph and the complete graph. We further show how this disorder-enhanced spreading is related to the networks' eigenvalues. [ABSTRACT FROM AUTHOR]

Summary: In this article we analyze in how far semiflexible behavior enhances the differences in the properties of classes of polymers whose topological structure varies. We focus on three pairs of macromolecular classes: stars vs. chains, unknotted rings vs. rings with one knot (trefoils), and stars vs. unknotted rings. For this we determine the mean-square radii of gyration and the bond-bond correlation functions through Monte Carlo simulations which use the bond fluctuation model. We show that introducing semiflexibility magnifies the differences between experimentally measurable quantities and may even lead to qualitative changes. Our simulation results are supported by theoretical studies which make use of the maximum entropy principle. [ABSTRACT FROM AUTHOR]

Recent findings suggest that processes such as the excitonic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy transfer one has to leave the classical, master-equation-type formalism and advance towards an increasingly quantum-mechanical picture, while still retaining a local description of the complex network of molecules involved in the transport, say through a tight-binding approach. Interestingly, the continuous time random walk (CTRW) picture, widely employed in describing transport in random environments, can be mathematically reformulated to yield a quantum-mechanical Hamiltonian of tight-binding type; the procedure uses the mathematical analogies between time-evolution operators in statistical and in quantum mechanics: The result are continuous-time quantum walks (CTQWs). However, beyond these formal analogies, CTRWs and CTQWs display vastly different physical properties. In particular, here we focus on trapping processes on a ring and show, both analytically and numerically, that distinct configurations of traps (ranging from periodical to random) yield strongly different behaviors for the quantal mean survival probability, while classically (under ordered conditions) we always find an exponential decay at long times. [ABSTRACT FROM AUTHOR]

A fundamental and long-standing problem in polymer physics is to deduce the relationship between the topology of a polymer and its dynamics. Generalized Gaussian structures (GGS), originating from the familiar Rouse model, represent a valuable tool for this purpose. This review summarizes theoretical efforts that have been undertaken in studying the dynamics of polymer systems with complex internal topologies by employing the GGS approach. The dynamic properties of a wide range of polymeric structures (ranging from polymer networks to dendritic and hybrid polymers) are discussed, while emphasizing systems that can be treated analytically (or semi-analytically). These studies provide considerable insight into the problem of relating the structure of a polymer to its dynamics. In many cases the GGS-treatment represents a first step in understanding the dynamics of polymers, and it may serve as a reference point for the development of more realistic models. [ABSTRACT FROM AUTHOR]

Focuses on equations built on fractional derivatives that allows physicists to describe systems with anomalously slow diffusion or subdiffusion. History of fractional integrals and derivatives; Description on the continuous-time random walks; Derivation of the Fokker-Planck equation; Applications of the fractional Fokker-Planck equation. INSET: Box 2. From Oliver Heaviside to Stress Moduli of Polymers.

Anomalous dynamics have been extensively investigated, especially in modelling charge transfer in photoconductivity and, more generally, for subballistic and superballistic transport, as found, say, in turbulent ionic motion in plasmas. In many such cases, work has focused on particles without internal degrees of freedom. Here we present models in which the anomalous dynamics is due to the internal modes of the moving particles, and less to the disorder of the medium or to the external fields. [ABSTRACT FROM AUTHOR]