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Hydrodynamic effect on the relaxation modes for a system of charged particles is reexamined. This effect is shown to produce a decrease in the diffusion coefficient due to the cloud of particles surrounding each charge. [ABSTRACT FROM AUTHOR]

Recent experiments by Brückner et al. [Science 380, 1357 (2023)] have observed an anomalous chain length dependence of the time of near approach of widely separated pairs of genomic elements on transcriptionally active chromosomal DNA. In this paper, I suggest that the anomaly may have its roots in internal friction between neighboring segments on the DNA backbone. The basis for this proposal is a model of chain dynamics formulated in terms of a continuum scaled Brownian walk (sBw) of polymerization index N. The sBw is an extension of the simple Brownian walk model widely used in path integral calculations of polymer properties, differing from it in containing an additional parameter H (the Hurst index) that can be tuned to produce varying degrees of correlation between adjacent monomers. A calculation using the sBw of the mean time τc for chain closure predicts-under the Wilemski-Fixman approximation for diffusion-controlled reactions-that at early times, τc varies as the 2/3 power of N, in close agreement with the findings of the Brückner et al. study. Other scaling relations of that study, including those related to the probability of loop formation and the mean square displacements of terminal monomers, are also satisfactorily accounted for by the model., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Polymer models describing the statistics of biomolecules under confinement have applications to a wide range of single-molecule experimental techniques and give insight into biologically relevant processes in vivo. In this paper, we determine the transverse position and bending correlation functions for a wormlike chain confined within slits and cylinders (with one and two confined dimensions, respectively) using a mean-field approach that enforces rigid constraints on average. We show the theoretical predictions accurately capture the statistics of a wormlike chain from Monte Carlo simulations in both confining geometries for both weak and strong confinement. We also show that the longitudinal correlation function is accurately computed for a chain confined to a slit and leverages the accuracy of the model to suggest an experimental technique to infer the (often unobservable) transverse statistics from the (directly observable) longitudinal end-to-end distance. [ABSTRACT FROM AUTHOR]

Polymer crystallization has long been a fascinating problem and is still attracting many researchers. Most of the previous simulations are concentrated on clarifying the universal aspects of polymer crystallization using model linear polymers such as polyethylene. We are recently focusing on a nearly untouched but very interesting problem of chiral selecting crystallization in helical polymers. We previously proposed a stepwise approach using two kinds of helical polymers, simple "bare" helical polymers made of backbone atoms only such as polyoxymethylene (POM) and "general" helical polymers containing complicated side groups such as isotactic polypropylene. We have already reported on the crystallization in oligomeric POM-like helix but have observed only weak chiral selectivity during crystallization. In the present paper, we investigate the crystallization of sufficiently long POM-like polymer both from the isotropic melt and from the highly stretched melt. We find in both cases that the polymer shows a clear chiral selecting crystallization. Specifically, the observation of a single crystal growing from the isotropic melt is very illuminating. It shows that the crystal thickness and the crystal chirality are closely correlated; thicker crystals show definite chirality while thinner ones are mostly mixtures of the R- and the L-handed stems. The single crystal is found to have a marked lenticular shape, where the thinner growth front, since being made of the mixture, shows no chiral selectivity. The final chiral crystal is found to be completed through helix reversal processes within thicker regions. [ABSTRACT FROM AUTHOR]

The two pulse fluorescence bleaching experiments reported in an earlier paper [J. Chem. Phys. 117, 454 (2002)] are reanalyzed in the context of additional experiments. The fluorescence bleaching observed in that paper was originally ascribed to ground-state depletion. By analyzing the absorption saturation behavior and the magnitude of the pump–probe signal, we find that the absorption cross section of poly(phenylene vinylene) at 400 nm is two orders of magnitude too small to significantly deplete the ground state given the pump fluences used in that experiment. Instead, the observed depletion is due to a combination of exciton–exciton annihilation at early times and dark state luminescence quenching at later times. Different experiments have different sensitivities to the fluence-dependent quenching, with time-resolved experiments like transient emission and fluorescence decay time consistently underestimating the exciton–exciton annihilation rate. Experiments that measure the integrated fluorescence, such as fluorescence saturation and bleaching, result in a consistent value for the exciton–exciton annihilation constant of 6×10[sup -9] cm[sup 3]/s, while the dark state quenching constant is estimated to be at least 1.2×10[sup -8] cm[sup 3]/s. Indirect evidence based on the wavelength and sample dependence of the dark state formation suggest that the dark states are charge-separated polarons. The relatively large quenching constants are consistent with what has been observed in other conjugated polymers and suggest that the long-lived dark states in particular are effective quenchers, capable of quenching thousands of surrounding chromophores. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations and measure the mean first-passage time t(z) for the free end to reach a certain distance z away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of t(z) are observed, with transition between them varying as a function of chain length. We use these simulation results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations leads us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more. [ABSTRACT FROM AUTHOR]

Motivated by the recent experimental observations of the DNA loop extrusion by protein motors, in this paper, we investigate the statistical properties of the growing polymer loops within the ideal chain model. The loop conformation is characterized statistically by the mean gyration radius and the pairwise contact probabilities. It turns out that a single dimensionless parameter, which is given by the ratio of the loop relaxation time over the time elapsed since the start of extrusion, controls the crossover between near-equilibrium and highly non-equilibrium asymptotics in the statistics of the extruded loop, regardless of the specific time dependence of the extrusion velocity. In addition, we show that two-sided and one-sided loop extruding motors produce the loops with almost identical properties. Our predictions are based on two rigorous semi-analytical methods accompanied by asymptotic analysis of slow and fast extrusion limits. [ABSTRACT FROM AUTHOR]

The thermodynamics of symmetric polymer blends is investigated using the polymer reference interaction site model integral equation theory with the new molecular closures presented in the previous paper. In contrast to the atomic mean spherical approximation reported earlier by Schweizer and Curro [J. Chem. Phys. 91, 5059 (1989); Chem. Phys. 149, 105 (1990)] (in which the critical temperature is proportional to the square root of the degree of polymerization), the molecular closures predict a linear dependence of the critical temperature on the degree of polymerization, in agreement with classical mean field theory. Detailed numerical calculations using the reference molecular mean spherical approximation (R-MMSA) and the reference molecular Percus–Yevick (R-MPY) closures are presented for the intermolecular structure and effective chi parameter in symmetric blends of semiflexible chains. For the symmetric blend, the R-MMSA closure is almost an integral equation realization of mean field theory, consistent with the analytical results presented in the previous paper. With the R-MPY closure, at low densities, the effective chi parameter is significantly renormalized down from its mean field value and displays a strong composition dependence. As the density is increased, both the renormalization of the effective chi parameter and its composition dependence become weaker. These trends are consistent with recent computer simulations. The influence of chain aspect ratio and the precise choice of intermolecular potentials on blend thermodynamics and phase separation are also explored. With the exception of the composition dependence of the effective chi parameter in the R-MPY theory, the analytical thread calculations are shown to be in qualitative, and sometimes quantitative, agreement with all the numerical results for symmetric blends. [ABSTRACT FROM AUTHOR]

The external voltage-driven polymer translocation through a conical pore (with a large opening at the entry and a small tip at the exit) is studied by using the Langevin dynamics simulation in this paper. The entire translocation process is divided into an approaching stage and a threading stage. First, the approaching stage starts from the polymer entering the large opening and ends up at a terminal monomer reaching the pore tip. In this stage, the polymer will undergo the conformation adjustment to fit the narrowed cross-sectional area of the pore, leading to three approaching modes: the non-stuck mode with a terminal monomer arriving at the pore tip smoothly, the weak-stuck mode for the polymer stuck inside the pore for a short duration with minor conformational adjustments, and the strong-stuck mode with major conformational changes and a long duration. The approaching times (the duration of the approaching stage) of the three approaching modes show different behavior as a function of the pore apex angle. Second, the threading stage describes that the polymer threads through the pore tip with a linear fashion. In this stage, an increase in the apex angle causes the reduction of the threading time (the duration of the threading stage) due to the increase in the driving force with the apex angle at the tip. Moreover, we also find that with the increase in the apex angle or the polymer length, the polymer threading dynamics will change from the quasi-equilibrium state to the non-equilibrium state. [ABSTRACT FROM AUTHOR]

Recent experiments on the return to equilibrium of solutions of entangled polymers stretched by extensional flows [Zhou and Schroeder, Phys. Rev. Lett. 120, 267801 (2018)] have highlighted the possible role of the tube model's two-step mechanism in the process of chain relaxation. In this paper, motivated by these findings, we use a generalized Langevin equation (GLE) to study the time evolution, under linear mixed flow, of the linear dimensions of a single finitely extensible Rouse polymer in a solution of other polymers. Approximating the memory function of the GLE, which contains the details of the interactions of the Rouse polymer with its surroundings, by a power law defined by two parameters, we show that the decay of the chain's fractional extension in the steady state can be expressed in terms of a linear combination of Mittag-Leffler and generalized Mittag-Leffler functions. For the special cases of elongational flow and steady shear flow, and after adjustment of the parameters in the memory function, our calculated decay curves provide satisfactory fits to the experimental decay curves from the work of Zhou and Schroeder and earlier work of Teixeira et al. [Macromolecules 40, 2461 (2007)]. The non-exponential character of the Mittag-Leffler functions and the consequent absence of characteristic decay constants suggest that melt relaxation may proceed by a sequence of steps with an essentially continuous, rather than discrete, spectrum of timescales. [ABSTRACT FROM AUTHOR]

In Paper I [T. J. H. Hele and S. C. Althorpe, J. Chem. Phys. 138, 084108 (2013)] we derived a quantum transition-state theory (TST) by taking the t → 0+ limit of a new form of quantum flux-side time-correlation function containing a ring-polymer dividing surface. This t → 0+ limit appears to be unique in giving positive-definite Boltzmann statistics, and is identical to ring-polymer molecular dynamics (RPMD) TST. Here, we show that quantum TST (i.e., RPMD-TST) is exact if there is no recrossing (by the real-time quantum dynamics) of the ring-polymer dividing surface, nor of any surface orthogonal to it in the space describing fluctuations in the polymer-bead positions along the reaction coordinate. In practice, this means that RPMD-TST gives a good approximation to the exact quantum rate for direct reactions, provided the temperature is not too far below the cross-over to deep tunnelling. We derive these results by comparing the t → ∞ limit of the ring-polymer flux-side time-correlation function with that of a hybrid flux-side time-correlation function (containing a ring-polymer flux operator and a Miller-Schwarz-Tromp side function), and by representing the resulting ring-polymer momentum integrals as hypercubes. Together with Paper I, the results of this article validate a large number of RPMD calculations of reaction rates. [ABSTRACT FROM AUTHOR]

In an extension of earlier studies from this group on the application of the Jarzynski equality to the determination of the elastic properties of a finitely extensible Rouse model of polymers under flow [A. Ghosal and B. J. Cherayil, J. Chem. Phys. 144, 214902 (2016)], we derive several new theoretical results in this paper on the nature of the distribution function P(w) that governs the long-time limit t>>1 of the fluctuations in the work w performed by the polymer during flow-induced stretching. In particular, we show that an expression for the average of the nth power of the work, 〈wn(t)〉, can be obtained in closed form in this limit, making it possible to exactly calculate three important statistical measures of P(w): the mean μ, the skewness γ1, and the kurtosis γ2 (apart from the variance σ²). We find, for instance, that to leading order in t, the mean grows linearly with t at a constant value of the dimensionless flow rate Wi and that the slope of the μ−t curve increases with increasing Wi. These observations are in complete qualitative agreement with data from Brownian dynamics simulations of flow-driven double-stranded DNA by Latinwo and Schroeder [Macromolecules 46, 8345 (2013)]. We also find that the skewness γ1 exhibits an interesting inversion of sign as a function of Wi, starting off at positive values at low Wi and changing to negative values at larger Wi. The inversion takes place in the vicinity of what we interpret as a coil-stretch transition. Again, the finding exactly reproduces behavior seen in other numerical and experimental work by the above group Latinwo et al. [J. Chem. Phys. 141, 174903 (2014)]. Additionally, at essentially the same value of Wi at which this sign inversion takes place, we observe that the kurtosis reaches a minimum, close to 1, providing further evidence of the existence of a coil-stretch transition at this location. Our calculations reproduce another numerical finding: a power law dependence on Wi of the rate of work production that is characterized by two distinct regimes, one lying below the putative coil-stretch transition, where the exponent assumes one value, and the other above, where it assumes a second. [ABSTRACT FROM AUTHOR]

In this paper, molecular dynamics simulations are used to study the effect of molecular water and composition (Si/Al ratio) on the structure and mechanical properties of fully polymerized amorphous sodium aluminosilicate geopolymer binders. The X-ray pair distribution function for the simulated geopolymer binder phase showed good agreement with the experimentally determined structure in terms of bond lengths of the various atomic pairs. The elastic constants and ultimate tensile strength of the geopolymer binders were calculated as a function of water content and Si/Al ratio; while increasing the Si/Al ratio from one to three led to an increase in the respective values of the elastic stiffness and tensile strength, for a given Si/Al ratio, increasing the water content decreased the stiffness and strength of the binder phase. An atomic-scale analysis showed a direct correlation between water content and diffusion of alkali ions, resulting in the weakening of the AlO4 tetrahedral structure due to the migration of charge balancing alkali ions away from the tetrahedra, ultimately leading to failure. In the presence of water molecules, the diffusion behavior of alkali cations was found to be particularly anomalous, showing dynamic heterogeneity. This paper, for the first time, proves the efficacy of atomistic simulations for understanding the effect of water in geopolymer binders and can thus serve as a useful design tool for optimizing composition of geopolymers with improved mechanical properties. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach to study the probability distribution of the radius of gyration of freely jointed chains. In this approach, we study the joint distribution PN(Rg2,Rvector G), where Rg is the radius of gyration and Rvector G is the vector from the first bead to the center of the chain. We derive an iteration relation between the probability distributions of chains with lengths N and N+1. When the chain length is large, the iteration relation can be approximated by an evolution equation with integral determining condition. The equation is solved to obtain the probability distribution function, which yields the known result obtained by Fixman [J. Chem. Phys. 36, 306 (1962)] using the integral method. We hope the iteration method in this paper could be used to study the probability distribution of the structure factor of polymer molecules. [ABSTRACT FROM AUTHOR]

The nonlinear viscoelastic behavior of the Fraenkel-chain model is studied with respect to the constitutive equation of the Rouse model. Distinctly different from the results of the Rouse model, the Fraenkel-chain model gives the following characteristic nonlinear behavior: (a) The two distinct dynamic modes in the relaxation modulus GS(t,λ)—as observed in the linear region reported in Paper I [Y.-H. Lin and A. K. Das, J. Chem. Phys. 126, 074902 (2007), preceding paper]—or in the first normal-stress difference function GΨ1(t,λ) are shown to have different strain dependences: strain hardening for the fast mode and strain softening for the slow mode. (b) The Lodge–Meissner relation GS(t,λ)=GΨ1(t,λ) holds over the whole time range, which has been shown both analytically and by simulation. (c) The second normal-stress difference is nonzero, being positive in the fast-mode region and negative in the slow-mode region. The comparisons between orientation and stress for all tensor components consistently confirm the strong correlation of the slow mode as well as its entropic nature with the segmental-orientation anisotropy as shown in the linear region studied in Paper I. A consequence of this correlation is the applicability of the stress-optical rule in the slow-mode region. This also leads to the expectation that the damping function h(λ)=GS(t,λ)/GS(t,λ→0) and the ratio between the first and second normal-stress differences, N2(t,λ)/N1(t,λ), are described by the orientation tensor which has the same form as that given by Doi and Edwards [J. Chem. Soc. Faraday Trans. 2 74, 1789 (1978); 74, 1802 (1978)] with independent-alignment approximation for an entangled system. The similarity between the slow mode of an entanglement-free Fraenkel-chain system and the terminal mode of an entangled polymer system as observed in the comparison of theory, simulation, and experiment suggests that the close correlation of the entropic nature of the mode with the orientation anisotropy—as of the Fraenkel segment or the primitive step in the Doi–Edwards theory—is a generally valid physical concept in polymer viscoelasticity. [ABSTRACT FROM AUTHOR]

We introduce a new, topologically-based method for coarse-graining polymer chains. Based on the wavelet transform, a multiresolution data analysis technique, this method assigns a cluster of particles to a coarse-grained bead located at the center of mass of the cluster, thereby reducing the complexity of the problem by dividing the simulation into several stages, each with a fraction of the number of beads as the overall chain. At each stage, we compute the distributions of coarse-grained internal coordinates as well as potential functions required for subsequent simulation stages. In this paper, we present the basic algorithm, and apply it to freely jointed chains; the companion paper describes its applications to self-avoiding chains. [ABSTRACT FROM AUTHOR]

Knowledge of the conformational evolution of a polymer chain provides invaluable information for all polymer properties. However, the chain evolution is usually determined by monitoring single beads for short times only. In this paper, we numerically determine the configuration evolution over extended time periods by monitoring the eigenvalues of the gyration tensor and applying the scaling law methodology. Results of Brownian dynamics simulations of initially straight chains reveal that after the early free transverse diffusion, flexible polymers exhibit a transverse intermediate-time behavior of t[sup 3/4], while stiff polymers reveal two intermediate-time behaviors: an early t[sup 5/6] power law accompanied by a late t[sup 3/4] evolution. These results are associated with the inherent nonlinearity of the problem. The scaling law methodology we develop in this paper for monitoring the chain configuration should have wide applications in the study of polymer rheology. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The loop formation of a single polymer chain has served as a model system for various biological and chemical processes. Theories based on the Smoluchowski equation proposed that the rate constant (kloop) of the loop formation would be inversely proportional to viscosity (η), i.e., kloop ∼ η−1. Experiments and simulations showed, however, that kloop showed the fractional viscosity dependence of kloop ∼ η−β with β < 1 either in glasses or in low-viscosity solutions. The origin of the fractional viscosity dependence remains elusive and has been attributed to phenomenological aspects. In this paper, we illustrate that the well-known failure of classical kinetics of the loop formation results from the breakdown of the local thermal equilibrium (LTE) approximation and that the mutual information can quantify the breakdown of the LTE successfully. [ABSTRACT FROM AUTHOR]

We use the two solvation potentials discussed in the previous paper and polymer reference interaction-site model (PRISM) theory to calculate the mutually consistent single-molecule conformation and liquid structure of model linear flexible nonpolar polymers. We focus on the mean end-to-end distance R2 and radius of gyration Rg of the single chain as functions of polymer density. Our calculations are compared to computer simulations to assess their accuracy, and some aspects of the general trends with density predicted are discussed. Two methods of calculating the conformation of the single chain in the solvation potential are used, one is Monte Carlo simulation, the other, introduced in this paper, employs a generating functional. We cannot unambiguously confirm the accuracy of one solvation potential over the other; at low density they give identical results, and the exact values are too few at high density. However, we are inclined to question the accuracy of the hypernetted-chain (HNC) style potential at high densities because it seems to predict a strong contraction of the polymer chain that is not seen experimentally in real polymer melts. [ABSTRACT FROM AUTHOR]

This paper discusses the effect of hydrodynamic interactions in multicomponent polymer systems. We show that the mobility matrix now has off diagonal elements when compared to the case where hydrodynamics is neglected. The wave vector dependence comes from the Oseen tensor which is convoluted with the static structure-factor matrix. The inclusion of Rouse mobilities is also discussed. [ABSTRACT FROM AUTHOR]

The general theory of the construction of scale-consistent energy terms in the coarse-grained force fields presented in Paper I of this series has been applied to the revision of the UNRES force field for physics-based simulations of proteins. The potentials of mean force corresponding to backbone-local and backbone-correlation energy terms were calculated from the ab initio energy surfaces of terminally blocked glycine, alanine, and proline, and the respective analytical expressions, derived by using the scale-consistent formalism, were fitted to them. The parameters of all these potentials depend on single-residue types, thus reducing their number and preventing over-fitting. The UNRES force field with the revised backbone-local and backbone-correlation terms was calibrated with a set of four small proteins with basic folds: tryptophan cage variant (TRP1; α), Full Sequence Design (FSD; α + β), villin headpiece (villin; α), and a truncated FBP-28 WW-domain variant (2MWD; β) (the NEWCT-4P force field) and, subsequently, with an enhanced set of 9 proteins composed of TRP1, FSD, villin, 1BDC (α), 2I18 (α), 1QHK (α + β), 2N9L (α + β), 1E0L (β), and 2LX7 (β) (the NEWCT-9P force field). The NEWCT-9P force field performed better than NEWCT-4P in a blind-prediction-like test with a set of 26 proteins not used in calibration and outperformed, in a test with 76 proteins, the most advanced OPT-WTFSA-2 version of UNRES with former backbone-local and backbone-correlation terms that contained more energy terms and more optimizable parameters. The NEWCT-9P force field reproduced the bimodal distribution of backbone-virtual-bond angles in the simulated structures, as observed in experimental protein structures. [ABSTRACT FROM AUTHOR]

In this paper, we study a system of entangled chains that bear reversible cross-links in a melt state. The cross-links are tethered uniformly on the backbone of each chain. A slip-link type model for the system is presented and solved for the relaxation modulus. The effects of entanglements and reversible cross-linkers are modelled as a discrete form of constraints that influence the motion of the primitive path. In contrast to a non-associating entangled system, the model calculations demonstrate that the elastic modulus has a much higher first plateau and a delayed terminal relaxation. These effects are attributed to the evolution of the entangled chains, as influenced by tethered reversible linkers. The model is solved for the case when the linker survival time τs is greater than the entanglement time τe, but less than the Rouse time τR. [ABSTRACT FROM AUTHOR]

Organic materials with a high index of refraction (RI) are attracting considerable interest due to their potential application in optic and optoelectronic devices. However, most of these applications require an RI value of 1.7 or larger, while typical carbon-based polymers only exhibit values in the range of 1.3–1.5. This paper introduces an efficient computational protocol for the accurate prediction of RI values in polymers to facilitate in silico studies that can guide the discovery and design of next-generation high-RI materials. Our protocol is based on the Lorentz-Lorenz equation and is parametrized by the polarizability and number density values of a given candidate compound. In the proposed scheme, we compute the former using first-principles electronic structure theory and the latter using an approximation based on van der Waals volumes. The critical parameter in the number density approximation is the packing fraction of the bulk polymer, for which we have devised a machine learning model. We demonstrate the performance of the proposed RI protocol by testing its predictions against the experimentally known RI values of 112 optical polymers. Our approach to combine first-principles and data modeling emerges as both a successful and a highly economical path to determining the RI values for a wide range of organic polymers. [ABSTRACT FROM AUTHOR]

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH4→ H2 + CH3. The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases. [ABSTRACT FROM AUTHOR]

We use the bond fluctuation model (BFM) to study the pore-blockade times of a translocating polymer of length N in two dimensions, in the absence of external forces on the polymer (i.e., unbiased translocation) and hydrodynamic interactions (i.e., the polymer is a Rouse polymer), through a narrow pore. Earlier studies using the BFM concluded that the pore-blockade time scales with polymer length as τd∼Nβ, with β=1+2ν, whereas some recent studies using different polymer models produce results consistent with β=2+ν, originally predicted by us. Here ν is the Flory exponent of the polymer; ν=0.75 in 2D. In this paper we show that for the BFM if the simulations are extended to longer polymers, the purported scaling τd∼N1+2ν ceases to hold. We characterize the finite-size effects, and study the mobility of individual monomers in the BFM. In particular, we find that in the BFM, in the vicinity of the pore the individual monomeric mobilities are heavily suppressed in the direction perpendicular to the membrane. After a modification of the BFM which counters this suppression (but possibly introduces other artifacts in the dynamics), the apparent exponent β increases significantly. Our conclusion is that BFM simulations do not rule out our theoretical prediction for unbiased translocation, namely, β=2+ν. [ABSTRACT FROM AUTHOR]

Disorder plays an important role in the photophysics of conjugated polymers such as poly(para-phenylene vinylene) (PPV). The dipole moments measured by electroabsorption spectroscopy for a centrosymmetric system such as PPV provide a direct quantitative measure of disorder-induced symmetry breaking. Although inner-sphere (structural) disorder is present, outer-sphere (environmental) disorder dominates the symmetry breaking in PPV. This paper develops and compares six models of outer-sphere disorder that differ in their representation of the electrostatic environment of PPV in glassy solvents. The most detailed model is an all-atom description of the solvent glass and this model forms the basis for comparison of the less detailed models. Four models are constructed in which multipoles are placed at points on a lattice. These lattice models differ in the degree to which they include correlation between the lattice spacings and the orientations of the multipoles. A simple model that assigns random Gaussian-distributed electrostatic potentials to each atom in the PPV molecule is also considered. Comparison of electronic structure calculations of PPV in these electrostatic environments using the all-atom model as a benchmark reveals that dipole and quadrupole lattices provide reasonable models of organic glassy solvents. Including orientational correlation among the solvent molecules decreases the effects of outer-sphere disorder, whereas including correlation in the lattice spacings increases the effects. Both the dipole and quadrupole moments of the solvent molecules can have significant effects on the symmetry breaking and these effects are additive. This additivity provides a convenient means for predicting the effects of various glassy solvents based on their multipole moments. The results presented here suggest that electrostatic disorder can account for the observed symmetry breaking in organic glasses. Furthermore, the lattice models are in general agreement with the dipole and quadrupole lattice models used to explain the Poole–Frenkel behavior in charge transport through disordered organic materials. [ABSTRACT FROM AUTHOR]

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time τ as function of the polymer length N: In the general expression τ∼Nβ/E, the exponent changes from β=1 for moderately long chains to β=1+ν or β=2ν for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains. [ABSTRACT FROM AUTHOR]

In this paper a Clifford algebra-based method is applied to calculate polymer chain conformations. The approach enables the calculation of the position of an atom in space with the knowledge of the bond length (l), valence angle (θ), and rotation angle (φ) of each of the preceding bonds in the chain. Hence, the set of geometrical parameters {li,θi,φi} yields all the position coordinates pi of the main chain atoms. Moreover, the method allows the calculation of side chain conformations and the computation of rotations of chain segments. With these features it is, in principle, possible to generate conformations of any type of chemical structure. This method is proposed as an alternative for the classical approach by matrix algebra. It is more straightforward and its final symbolic representation considerably simpler than that of matrix algebra. Approaches for realistic modeling by means of incorporation of energetic considerations can be combined with it. This article, however, is entirely focused at showing the suitable mathematical framework on which further developments and applications can be built. [ABSTRACT FROM AUTHOR]

The rheological behaviors of polymer brush under oscillatory shear flow were investigated by nonequilibrium Monte Carlo simulation. The grafted chain under oscillatory shear flow exhibited a waggling behavior like a flower, and the segments were found to have different oscillatory phases along the chain contour. Stress tensor was further obtained based on the statistics of sampled configuration distribution functions. The simulation reproduced the abrupt increase of the first normal stress difference N1 with the flow velocity over a critical value, as observed in the experiment of Klein et al. [Nature (London) 352, 143 (1991)]. However, our simulation did not reproduce the brush thickening with shear velocity increased, which was suggested to be responsible for the abrupt increase of N1 in the above-mentioned paper. This simulation demonstrates that the increase of normal stress might be an inherent behavior of polymer brush due to chain deformation under flow. [ABSTRACT FROM AUTHOR]

The paper presents a combined experimental and theoretical approach to the understanding of hysteresis and adhesion contributions to rubber friction on dry and lubricated rough surfaces. Based on a proper analysis of the temperature- and frequency-dependent behaviors of nonlinear viscoelastic materials such as filler reinforced elastomer materials, master curves for the viscoelastic moduli are constructed. It is shown that the classical williams–Landel–Ferry equation cannot be applied in its simple form, but needs the introduction of an energy term describing the temperature dependency of glassy polymer bridges, which transmit the forces within flocculated filler clusters. The activation energy for carbon black and silica-filled elastomers is compared based on two different evaluation methods. The obtained dynamic data are shown to be related to a different friction behavior of elastomers regarding the two filler systems. Theoretical predictions of the stationary frictional behavior of the systems are in fair agreement with the experimental friction data at low sliding velocities. It is found that the formulated adhesion plays a dominant role on rough dry surfaces within this range of velocities. [ABSTRACT FROM AUTHOR]

In this paper we consider the essential electronic excited states in parallel chains of semiconducting polymers that are currently being explored for photovoltaic and light-emitting diode applications. In particular, we focus upon various type II donor-acceptor heterojunctions and explore the relation between the exciton binding energy to the band offset in determining the device characteristic of a particular type II heterojunction material. As a general rule, when the exciton binding energy is greater than the band offset at the heterojunction, the exciton will remain the lowest-energy excited state and the junction will make an efficient light-emitting diode. On the other hand, if the offset is greater than the exciton binding energy, either the electron or hole can be transferred from one chain to the other. Here we use a two-band exciton to predict the vibronic absorption and emission spectra of model polymer heterojunctions. Our results underscore the role of vibrational relaxation and suggest that intersystem crossings may play some part in the formation of charge-transfer states following photoexcitation in certain cases. [ABSTRACT FROM AUTHOR]

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the relaxation dynamics of Sierpinski hexagon fractal polymer. The relaxation dynamics of this fractal polymer is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, by performing real-space renormalization transformations, we determine analytically the complete eigenvalue spectrum of the connectivity matrix. Based on the eigenvalues obtained through iterative algebraic relations we calculate the averaged monomer displacement and the mechanical relaxation moduli (storage modulus and loss modulus). The evaluation of the dynamical properties in the Rousetype approach reveals that they obey scaling in the intermediate time/frequency domain. In the Zimm-type approach, which includes the hydrodynamic interactions, the relaxation quantities do not show scaling. The theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results. [ABSTRACT FROM AUTHOR]

Morphology of symmetric ABCD tetrablock quaterpolymers in melt was studied by the Monte Carlo (MC) simulation, where the volume fractions of the block chains, f, kept the relationships of fA = fD and fB = fC, and the volume fraction of the two mid-blocks φ was defined as φ = fB + fC. Previous self-consistent field theory for ABCD reported morphological change including several structures; however, the scope was limited within a two-dimensional system. To the contrary, in this paper, MC simulations were carried out in three dimensions with changing the φ value finely, which resulted in finding a tetracontinuous structure in the range of 0.625 ⩽ φ ⩽ 0.75. Moreover the tetracontinuous structure has been found to be the gyroid structure, and the mean curvature of the B/C interface is nearly zero. We concluded that the B/C interface must be the Schoen gyroid surface, one of three-dimensional periodic minimal surfaces. The geometrical nature of the A/B interface should be equivalent to that of the C/D interface, and they stand as level surfaces to the Schoen gyroid surface. [ABSTRACT FROM AUTHOR]

In this paper, we continue investigations on the solution methods for the generalized Percus–Yevick equations for the pair correlation functions of polymers, which were formulated in the previous papers of this series [J. Chem. Phys. 99, 4084, 4103 (1993)]. Previously, they were reduced to recursive integral equations and solved numerically. In this paper, a translational invariance approximation is used to reduce the number of integral equations to solve. In this approximation, only N integral equations out of N2 integral equations are required for a polymer consisting of N beads (monomers). The behavior of an isolated polymer is studied with three different potential models, a soft sphere, a hard sphere, and a Lennard-Jones potential. The main motivation for considering these three potential models is in testing the idea of universality commonly believed to hold for some properties of polymers. We find that the universality holds for the power law exponent for the expansion factor of polymers at high temperatures. The end-to-end distance distribution functions, intermediate distribution functions, chemical potentials, the density distributions, and various expansion factors of the polymer chain are computed from the solutions of the integral equations in the case of coiled, ideal, and collapsed states of the polymer. The expansion factors in the collapsed regime are found to obey power laws with respect to the length of the polymer and [B(T)-B(θ)], where B(T) is the second virial coefficient and θ is a modified θ temperature. The values of these exponents approach those from the known theories of polymer collapse as the chain length becomes long and the ratio of bond length to bead radius becomes large. [ABSTRACT FROM AUTHOR]

In hydrogen-bonded polymer blends there are long range correlations that are a result of the combined covalent and hydrogen-bond connections. A mean field description of these mixtures is presented which indicates that there should be an infinite correlation length above some percolation threshold. There are various consequences of the compositional heterogeneities or clustering that results from these effects and these are discussed in this paper. [ABSTRACT FROM AUTHOR]

A recursive integral equation for the intramolecular correlation function of an isolated linear polymer of N bonds is derived from the integral equations presented in the preceding paper. The derivation basically involves limiting the density of the polymer to zero so that polymers do not interact with each other, and thus taking into account the intramolecular part only. The integral equation still has the form of a generalized Percus–Yevick integral equation. The intramolecular correlation function of a polymer of N bonds is recursively generated by means of it from those of polymers of 2, 3,..., (N-1) bonds. The end-to-end distance distribution functions are computed by using the integral equation for various chain lengths, temperatures, and bond lengths in the case of a repulsive soft-sphere potential. Numerical solutions of the recursive integral equation yield universal exponents for the mean square end-to-end distance in two and three dimensions with values which are close to the Flory results: 0.77 and 0.64 vs Flory’s values 0.75 and 0.6 for two and three dimensions, respectively. The intramolecular correlation functions computed can be fitted with displaced Gaussian forms. The N dependence of the internal chemical potential is found to saturate after some value of N depending on the ratio of the bond length to the bead radius. [ABSTRACT FROM AUTHOR]

We present a self-consistent-field structure for the thermodynamic description of concentrated solutions of liquid-crystal polymers. The polymers are assumed to be locally stiff but capable of curvature over large distances. The formulation of the chain geometry is that of a wormlike polymer, but the final analysis is simpler than the Kratky–Porod form. The phase behavior is analyzed for a cylindrically symmetric mean-field nematic ordering interaction. As expected, in two dimensions the system undergoes a second-order phase transition and in three dimensions the nematic transition is first-order uniaxial. The three relevant physical parameters which describe the phase behavior of the polymers are the molecular mass of the polymers, a measure of the chain stiffness and strength of the nematic interaction. The formulation in this paper is for infinitely long polymers. If the chain stiffness is measured by the bending energy ε, with u as the strength of the hardcore repulsion and U that of the soft interactions, we find the following relationship at the isotropic-nematic transition: ccβcε(u+Uβc)=6. cc is the critical concentration and βc=1/kBTc is the inverse critical temperature. At the transition we find that the order parameter has a universal value of 0.25. We present universal plots for the order parameter and free energy of the system as a function of polymer concentration and temperature. [ABSTRACT FROM AUTHOR]

The two-dimensional (2D) exchange nuclear magnetic resonance (NMR) experiment is applied to study ultraslow as well as faster chain motions in amorphous polymers in the glass transition range. Acquisition of the time domain data with a four-pulse sequence leads to new characteristics in the corresponding 2H 2D line shapes if the correlation times of the motion are in the intermediate dynamic range. From the asymmetric 2D line shapes, the width of the correlation time distribution can be determined with higher accuracy than through conventional 1D NMR methods. Experimental data are presented on two amorphous polymers—atactic polypropylene and cis-1,4-polyisoprene—and are analyzed in terms of isotropic rotational diffusion. Deviations from this simple model due to the presence of conformational transitions within the polymer backbone are detected. Close to Tg, the mean correlation times extracted from 2D exchange NMR exhibit strongly nonArrhenius behavior usually described by the Williams–Landel–Ferry (WLF) equation. In addition, the width of the correlation time distribution is found to decrease with increasing temperature. [ABSTRACT FROM AUTHOR]

In this paper the Brownian dynamics technique for computer simulation of the fracture of polymer chains in a dilute solution subjected to elongational flow was used. Individual randomly coiled chains are placed at the stagnation point of a steady, uniaxial flow, and their evolution with time is monitored for chain fracture. The chains are modeled either as Rouse chains with a cutoff spring length, or as chains of springs obeying a Morse potential. Kinetic parameters are the first-order kinetic constant and the half-life time. The dependence of these parameters with elongational rate and chain length is expressed in the form of scaling laws, and the results are compared for the two models. Also studied was the size distribution of the resulting fracture fragments, finding that it may vary from sharply peaked to uniform, depending on the strength of the flow. [ABSTRACT FROM AUTHOR]

An analytical model of equilibrium phase separation in a mixture of two polymers in a common good solvent is developed, and its predictions compared with the results of a lattice simulation of the same system. The model combines the Landau–Ginzburg–Wilson formalism of two earlier papers (avoiding certain ad hoc assumptions introduced there) with the known scaling results of renormalization group calculations on critical fluids to derive expressions for the exponents that characterize the amplitudes of the singular temperature functions of various thermodynamic properties of the solution. The values so obtained for these exponents compare favorably with the data from the simulation, and considerably improve upon the predictions of simple scaling analyses. [ABSTRACT FROM AUTHOR]

The behavior of monomer density profiles of a star polymer in a d-dimensional good solvent, which was predicted in an earlier paper using scaling arguments, is now derived by using the renormalization group ε=4-d expansion method. Both the case of a free star in the bulk and of a center-adsorbed star at a free surface are considered. In the latter case of a semi-infinite problem, a distinction is made between repulsive walls, attractive walls—where for large arm length l, the configuration of the star is quasi-(d-1)-dimensional—and ‘‘marginal walls,’’ where for l→∞ the transition from d-dimensional to (d-1)-dimensional structure occurs. For free stars, ρ(r) behaves as r-d+1/ν for small r, where ν is the exponent describing the linear dimensions of the star, e.g., the gyration radius Rgyr∼lν. For center-adsorbed stars at repulsive or marginal walls, ρ(r||,z) behaves as ρ(r||,0)∼r-d+λ( f )|| and ρ(0,z)∼z-d+1/ν, where r|| and z denote the distances parallel and perpendicular to the surface, respectively; the new exponent λ( f ) depends explicitly on the number of arms f in general. We calculate this exponent λ( f ) to first order in ε=4-d; then λ( f ) is obtained to be (f-1)ε/4+O(ε2) for repulsive walls and 2-ε/4+O(ε2) for marginal walls. [ABSTRACT FROM AUTHOR]

The possibility of the existence of a 31 helix as a stable phase for poly(vinylidene fluoride) is investigated on the basis of intrachain and interchain interactions. The stable phase for PVF2 at low temperatures is well known to be the α phase, with a conformation of tgtg’, even though a calculation of the intrachain energy of a hypothetical helix leads to a value lower than that of the α phase. In this paper we discuss how the interchain energy acts to make the α phase the more stable conformation. Ingredients in this calculation include the compactness of chain packing and the results of imposing the condition of commensurability on the chain structure. [ABSTRACT FROM AUTHOR]

Using nuclear reaction analysis, we have measured the enrichment by one of the components at the surface of a binary mixture of random olefinic copolymers, with components of monomer structure E1-x1EEx1 and E1-x2EEx2. Here E and EE are the linear ethylene and branched ethylethylene groups (C4H8) and [C2H3(C2H5)], respectively, and x represents the fraction of the EE group randomly distributed on the chains. We examined 12 different couples covering a range x=0.38–0.97. The mixtures, whose thermodynamic behavior was established in our earlier paper, were cast in the form of films on both a silicon and on a gold-covered silicon surface, and were investigated in the one-phase region of the binodal in the vicinity of the critical temperature. We find that it is always the more flexible component—the one with a shorter statistical step length, corresponding to the higher ethylethylene fraction (higher x)—that is enriched at the polymer/air surface. Within our resolution neither component is enriched at the polymer/solid interface. These results show clearly that enthalpic rather than entropic factors dominate the surface potential driving the surface enrichment. For two of the mixtures we determined the excess of the surface-preferred species as a function of mixture composition along an isotherm in the one-phase region of the binodal. A consistent description of our data in terms of a mean-field model is provided by including in the surface potential a term in the mixture composition gradient at the polymer surface. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper discusses the behavior of melts of polymeric fractals in their dense state. It is shown that melts of polymeric fractals of spectral dimension D behave differently when D exceeds a critical value, i.e., DS=2d/(2+d). Here d is the dimension of space. For larger connectivities the fractals are saturated, whereas fractals with smaller connectivity behave similarly to melts of linear polymer chains. In the latter case the polymers interpenetrate each other to a great extent, screen their excluded volume, and retain their ideal shape. This conclusion is drawn by studying screening processes in melts of polymeric manifolds of arbitrary connectivity. It is shown that for systems above the critical spectral dimension a screening length exists, i.e., in other words, a concentration, for which the screening condition can never be satisfied. It is shown that this fact corresponds to saturation. Below the critical connectivity dimension the classical excluded volume screening—comparable to the case in linear polymer chains—takes place. The condition on the spectral dimension is equivalent to a condition in terms of the Gaussian fractal dimension df=2D/(2-D), i.e., the melt saturates when the embedding space dimension is less or equal than the Gaussian fractal dimension, i.e., d≤df. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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]

Although the Williams-Landell-Ferry (WLF) equation for the segmental relaxation time T(T) of glass-forming materials is one of the most commonly encountered relations in polymer physics, its molecular basis is not well understood. The WLF equation is often claimed to be equivalent to the Vogel-Fulcher-Tammann (VFT) equation, even though the WLF expression for T(T) contains no explicit dependence on the fragility parameter D of the VFT equation, while the VFT equation lacks any explicit reference to the glass transition temperature Tg, the traditionally chosen reference temperature in the WLF equation. The observed approximate universality of the WLF parameters C1(g) and C2(g) implies that T(T) depends only on T-Tg, a conclusion that seems difficult to reconcile with the VFT equation where the fragility parameter D largely governs the magnitude of T(T). The current paper addresses these apparent inconsistencies by first evaluating the macroscopic WLF parameters C1(g) and C2(g) from the generalized entropy theory of glass-formation and then by determining the dependence of C1(g) and C2(g) on the microscopic molecular parameters (including the strength of the cohesive molecular interactions and the degree of chain stiffness) and on the molar mass of the polymer. Attention in these calculations is restricted to the temperature range (Tg < T < Tg + 100 K), where both the WLF and VFT equations apply. [ABSTRACT FROM AUTHOR]

Most theories of the binding of molecules to surfaces or for the association between molecules treat the binding species as structureless entities and neglect their rigidity and the changes in their stiffness induced by the binding process. The binding species are also taken to be "ideal," meaning that the existence of van der Waals interactions and changes in these interactions upon molecular binding are also neglected. An understanding of the thermodynamics of these multifunctional molecular binding processes has recently come into focus in the context of the molecular binding of complex molecules, such as dendrimers and DNA grafted nanoparticles, to surfaces where the degree of binding cooperativity and selectivity, as well as the location of the binding transition, are found to be sensitive to the number of binding units constrained to a larger scale polymeric scaffold. We address the fundamental problem of molecular binding by extending classical Langmuir theory to describe the particular example of the reversible binding of semiflexible polymer chains to a solid substrate under melt conditions. The polymer chains are assumed to have a variable number N of binding units (segments) and to exhibit variable bending energies and van der Waals interactions in the bulk and on the surface, in addition to strong directional interactions with the surface. The resulting generalized Langmuir theory is applied to the examination of the influence of the chain connectivity of ideal polymers on the surface coverage Θ, transition binding temperature T 1/2 at which Θ = 1/2, and on the derivative |dΘ/dT| T=T 1/2 and the constant volume specific heat of binding, C v , measures of the cooperativity and "sharpness" of the binding transition, respectively. Paper II is devoted to the impact of the van der Waals attractive interactions and chain stiffness on the reversible binding of nonideal polymer chains to a solid surface, including the enthalpy-entropy compensation phenomenon observed experimentally in many molecular and particle binding processes.bind , measures of the cooperativity and "sharpness" of the binding transition, respectively. Paper II is devoted to the impact of the van der Waals attractive interactions and chain stiffness on the reversible binding of nonideal polymer chains to a solid surface, including the enthalpy-entropy compensation phenomenon observed experimentally in many molecular and particle binding processes.

Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results. [ABSTRACT FROM AUTHOR]