Search

This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete nonlinear dynamics. It is found that Markovian treatments based on a Wilemski-Fixman approximation significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics. In addition, this analysis provides scaling laws of the mean first cyclization time (MFCT) with the polymer size N and capture radius b, which are identical in both Markovian and non-Markovian approaches. In particular, it is found that the scaling of the MFCT for large N is given by T - N3/2ln(N/b²), which differs from the case of the Rouse dynamics where T - N². The extension to the case of the reaction kinetics of a monomer of a Zimm polymer with an external target in a confined volume is also presented. [ABSTRACT FROM AUTHOR]

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 molecular dynamics study of the dynamic scaling behavior of linear polymers in solution and in the melt when their character changes from fully flexible to semiflexible. The stiffness of the chains is determined by a bending potential. It is shown that the relaxation times τp characterizing the internal dynamics of the polymer chains as well as the mean square mode amplitudes ≤χp2≥ exhibit a clear crossover from Rouse to bending modes with increasing mode number p. For small mode numbers p the well-known p-2 Rouse behavior is observed, whereas large mode numbers exhibit the p-4 scaling, typical of the bending modes of semiflexible chains. We study the extension and the onset of the region where the crossover from p-2 to p-4 behavior occurs. With increasing stiffness of the chains we observe a shift of the crossover domain to smaller p-values. We also investigate the effect of chain stiffness on the monomer dynamics, based on their mean square displacements. Finally, we compare our results to previous simulations, where the scaling behavior of semiflexible chains was studied and which were restricted to a smaller range of persistence lengths lp and p values. [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 investigate hyperbranched polymers (HBPs) and highlight the relation between their architecture and their viscoelastic behavior, while paying special attention to the role of the chainlike spacer segments between branching points. For this we study the dynamics of HBP in solution, based on the generalized Gaussian structure formalism, an extension of the Rouse model, which disregards hydrodynamical and excluded volume effects. For HBP the dynamical effects display, beside the obvious contributions of localized modes on the spacers, also remarkable features, as we highlight based on the exact renormalization procedure recently developed by us in J. Chem. Phys. 123, 034907 (2005). We exemplify these features by analyzing the dynamics of randomly linked star polymers and study the impact both of the length and of the spacers’ mobility on the normal modes’ spectra. We compute these modes both by numerical diagonalization and also by employing our renormalization procedure; the excellent agreement between these methods allows us to extend the range of investigations to very large HBP. [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]

In this work we focus on the dynamics of macromolecular networks formed by end-linking identical polymer stars. The resulting macromolecular network can then be viewed as consisting of spacers which connect branching points (the cores of the stars). We succeed in analyzing exactly, in the framework of the generalized Gaussian model, the eigenvalue spectrum of such networks. As applications we focus on several topologies, such as regular networks and dendrimers; furthermore, we compare the results to those found for regular hyperbranched structures. In so doing, we also consider situations in which the beads of the cores differ from the beads of the spacers. The analytical procedure which we use involves an exact real-space renormalization, which allows to relate the star network to a (much simpler) network, in which each star is reduced to its core. It turns out that the eigenvalue spectrum of the star-polymer structure consists of two parts: one follows in terms of polynomial equations from the relaxation spectrum of the corresponding renormalized structure, while the second part involves the motion of the spacer chains themselves. Finally, we show exemplarily the situation for copolymeric dendrimers, calculate their spectra, and from them their storage and the loss moduli. [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]

We present a theoretical study of polymer networks, formed by connecting dendritic building blocks (DBB’s). We concentrate on the Rouse dynamics of such networks and perform our study in two steps, considering first single generalized dendrimers (GD’s) and then networks formed by such DBB’s. In GD’s the functionality f of the inner branching points may differ from the functionality f[sub c] of the core. The GD’s cover wide classes of macromolecules, such as the “classical” dendrimers (f[sub c]=f ), the dendritic wedges (f[sub c]=f-1), and the macromolecular stars (f[sub c]>2, f=2). Here we present a systematic, analytic way which allows us to treat the dynamics of individual GD’s. Then, using a general approach based on regular lattices formed by identical cells (meshes) we study the dynamics of GD-based polymer networks. Using analytical and numerical methods we determine the storage and loss moduli, G[sup ′](ω) and G[sup ″](ω). In this way we find that the intradendrimer relaxation domain of G[sup ′](ω) becomes narrower when M[sub cr], the number of connections between the neighboring DBB’s, increases. This effect may be understood due to the exclusion of the longest DBB relaxation times from the spectrum of the network, given that the additional connections hinder the mobility of the peripheral DBB branches. We expect that such effects may be readily observed through appropriate mechanical experiments. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We numerically analyze the scaling behavior of experimentally accessible dynamical relaxation forms for networks modeled through finite Sierpinski-type lattices. Previous work has established unequivocally for such lattices that in the Rouse picture both the mechanical and the dielectric relaxation forms scale in frequency and in time. As we show here, in the Zimm model, based on the preaveraged Oseen tensor, the picture changes drastically; the introduction of the hydrodynamic interactions leads to relaxation patterns which do not scale. Our results show that the relaxation forms are very sensitive to the number of monomers in the network and to the strength of the hydrodynamic interaction parameter. [ABSTRACT FROM AUTHOR]

We investigate on small world networks (SWN's) the survival probability of immobile targets, which get annihilated by random walkers at first encounter. On SWN's we find (distinct from regular lattices, Cayley trees, and regular ultrametric spaces) that in general the survival probability cannot be directly related to the average number of distinct sites visited. We underline this finding with arguments related to the structural disorder of SWN's and through the derivation of a lower bound for the targets' decay. [ABSTRACT FROM AUTHOR]

We focus on the dynamical properties of dendrimers and of randomly built branched polymers, which allows us to assess theoretically the role of disorder on the relaxation forms. We model the random polymers through a stochastic growth algorithm. Our studies are carried out both in the Rouse and also in the Zimm framework; the latter accounts for hydrodynamic interactions. Moreover, we also mimic the local geometry by imposing conditions on the average values of the angles between neighboring segments. Excluded volume interactions, however, are neglected throughout. The storage G′(ω) and the loss G″(ω) moduli, which we calculate, turn out to depend more on the hydrodynamic and the angular restrictions than on randomness. Furthermore, we find that both the randomness and the angular restrictions slow down the relaxation. Given that G′(ω), G″(ω) and also C(t), a function related to the radius of gyration, are all connected to the relaxation function G(t), a fact which we recall, we also calculate numerically G(t) and C(t); moreover we fit, following previous works, C(t) to stretched-exponential forms. Interestingly, it appears that from all functions considered G(t) is most sensitive to disorder. [ABSTRACT FROM AUTHOR]

The mechanical and dielectric relaxation of polymer networks depends (especially in simple Gaussian-type approaches which extend the Rouse model) on the eigenvalues of the corresponding connectivity matrices. We use this to evaluate explicitly experimentally accessible relaxation forms for finite Sierpinski-type networks, whose eigenvalue spectra are multifractal. It turns out that the observable quantities are by far less singular than the eigenvalue spectra, since the underlying spectral structures get smoothed out. Our results establish unequivocally the spectral dimension as fundamental relaxation parameter; to see this, however, the finite fractal networks have to be sufficiently large. © 2002 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.

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 consider the behavior of polyampholytes (PAs; heteropolymers carrying quenched positive and negative charges along the backbone) in external electrical fields. Whereas our previous treatments were devoted to the regime of a weak coupling of the charges, we consider here the regime where the electrostatic interactions between the charged monomers play the dominant role. Starting from a fluid drop picture we estimate the critical value of the external field that induces a breakup of the structure. As we proceed to show by scaling arguments, in strong fields the PA stretches out to a highly extended form, for which only a small fraction of the material is still organized in mesoscopic condensates along the rodlike configuration. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We extend our previous treatment [J. Chem. Phys. 103, 5070 (1995)] of polyampholytes (PAs, polymers with positively and negatively charged monomers) in an external field E, by modeling the PAs through freely jointed chains. Former works, based on Rouse-type models are linear, and hence are limited to sufficiently small values of E. The freely jointed chain model allows to consider the PAs conformations for E arbitrary. We calculate the PAs end-to-end distance for several charge distributions along the chain, which may be either ordered or random. For small E we recover previous results; large E-values lead to a crossover to stretched chain configurations, which depend crucially on the distribution of charges along the chain. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the direct incoherent energy transfer in systems, in which the molecules involved in the transfer process are attached to ideal (Gaussian) polymers, randomly arranged in a viscous solvent. In what the molecules’ attachment to polymers is concerned we consider two different situations: (a) each polymer chain contains at its opposite ends a donor and an acceptor molecule, (b) the donor molecules are dispersed randomly in the solvent and all acceptors are attached to polymers. In both cases we derive the donors’ decay forms exactly. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A phenomenological approach, which takes into account the basic geometry and the topology of fractal lattices and of branched polymers, is used to derive a new expression for the Flory exponent describing the average radius of gyration of branched polymers on fractals. The mean-field version of this formula nicely reproduces the values of the Flory exponent, calculated using real-space renormalization group methods on several fractal lattices. This technique also allows the determination of the scaling exponent of the radius of gyration of branched polymers without excluded-volume interactions on fractal lattices. As an application, the findings are exemplified by analyzing the direct, incoherent energy transfer (via multipolar interactions and exchange) from excited donors to acceptors, which are attached to branched polymers. [ABSTRACT FROM AUTHOR]

In this work we study the direct, incoherent energy transfer from excited donors to acceptors, which are attached to chainlike polymers. We consider both multipolar and exchange-type interactions between the donors and the acceptors. The polymers are modeled through random walks (Gaussian or self-avoiding, depending on the solvent). With the use of the end-to-end distribution function of the walks, we calculate the time dependence of the ensemble averaged decay of the excitation of the donor. For multipolar and exchange-type interactions, we find Kohlrausch–Williams–Watts (KWW) stretched exponential and exponential–logarithmic decay patterns, respectively. The decay forms reflect the quality (good or poor) of the solvent directly and they may be used to test transitions in the polymer conformation. [ABSTRACT FROM AUTHOR]

Examines the kinetic conditions of bimolecular based on catalytically activated reactions (CAR). Identification of elementary reaction act between reactants; Association between CAR and Collins Kimball type idea; Discussion on the characteristics of the catalytic site.

We study the kinetics of the A+A→0 and the A+B→0 diffusion-limited reactions by modeling the dynamics through random walks on ultrametric spaces, which allow to account for energetic randomness and to incorporate effects due to changes in temperature. We treat both pseudounimolecular (target and trapping) problems, as well as bimolecular reactions, and we compare the results to those which obtain for reactions on regular lattices and on fractals. Furthermore we analyze the possibility of describing reactions on ultrametric spaces through extensions of Smoluchowski-type approaches, and we show the limitations of such schemes when, as a function of temperature and of the reaction progress, the fluctuations in the particle densities get large. [ABSTRACT FROM AUTHOR]

We investigate the direct energy transfer from a donor to acceptors embedded in spaces with restricted geometries. The decay of the donor is expressed in terms of a site density function ρ0(r) which depends on the position of the donor within the structure. For randomly distributed donors one has to average over their locations. We focus on spherical and cylindrical shapes. The geometrical restrictions manifest themselves in deviations from the known Förster direct transfer behavior. [ABSTRACT FROM AUTHOR]

We study the kinetics of the A+A → P and the A+B → P diffusion-limited reactions by modeling the dynamics through random walks on regular and on fractal lattices. For the pseudounimolecular reactions A(0)≪B(0) we present exact analytical expressions for the target (DA=0) and the trapping (DB=0) problems. The kinetics of trapping as well as of the bimolecular reactions are then determined through simulation calculations. In all cases, we relate the results to Smoluchowski-type forms. Whereas the target and the A+A → P problems are well described by such forms, the trapping and the strictly bimolecular A+B → P reaction show different behaviors at longer times, due to fluctuations in the particle densities. [ABSTRACT FROM AUTHOR]