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Register a new userPersistence Length of Flexible Polyelectrolyte Chains
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We calculate the dependence of the electrostatic persistence length, l_e, of weakly charged flexible polyelectrolyte chains using a self-consistent variational theory. The variation of l_e with kappa, the inverse Debye screening length, is controlled by the parameter l_0 l_B/A^2, where l_0 is the bare persistence length, l_B is the Bjerrum length, and A is the mean distance between charges along the chain. Several distinct regimes for the dependence of l_e on kappa emerge depending on the value of l_0 l_B/A^2. We show that when l_0 l_B /A^2 << 1 we recover the classical result, l_e propto kappa^{-2}. For intermediate values of l_0 l_B /A^2, l_e propto kappa^{-1}. In this regime one can also get l_e propto kappa^{-y} with y < 1 depending on the strength of the Coulomb interaction. Qualitative comparisons between our theory and simulations as well as other theories are presented.
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The thermodynamic and elastic properties of a flexible polymer in the presence of dipole interactions are studied via Monte Carlo simulations. The structural coil-globular, solid-globular, and solid-solid transitions are mapped in the hyperphase diagram, parameterized by the dipole concentration, $eta$, and temperature, $T$. Polymer flexibility is usually quantified by the persistent length, $ell_p$, which is defined as the length on which the bond-bond correlation is lost. Non-monotonic flexibility of polymeric complexes as a function of $eta$ has been interpreted as a cooperative effect under the Worm-Like Chain model. Instead of the usual exponential behavior, $langle Cleft(kright)ranglepropto e^{-k/ell_p}$, here we show that the bond-bond correlation follows a power law decay, $langle Cleft(kright)rangleapprox c_0k^{-omega}$. The power law regime holds even at the coil-globular transition, where a Gaussian limit is expected, originated from non-leading terms due to monomer-monomer connectivity. The exponent $omega$ monotonically converges to the mbox{SAW} limit for large $eta$, if the isotherm pathway is constructed at the coil phase. The deviation from ideality in better probed at the chain segment size, and the expected $Theta-$condition at the $(T,eta)$ pathway near the coil-globular transition is not observed.
This paper discusses the elastic behavior of a single polyelectrolyte chain. A simple scaling analysis as in self avoiding walk chains are not possible, because three interplaying relevant length scales are involved, i.e., the Debye screening length and the Pincus blob size. Therefore a selfconsistent computation of an effective variational propagator is employed. It is shown that the elastic force f is proportional to the end to end distance R for small f. For larger forces we find a new regime, characterized by deformations larger than a computed electrostatic blob size. These results are supported by simulations and intuitive physical arguments.
We present a scheme to accurately calculate the persistence probabilities on sequences of $n$ heights above a level $h$ from the measured $n+2$ points of the height-height correlation function of a fluctuating interface. The calculated persistence probabilities compare very well with the measured persistence probabilities of a fluctuating phase-separated colloidal interface for the whole experimental range.
Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the molecular beam epitaxy (MBE) universality class. Both the initial transient and the long-time steady-state regimes are investigated. We show that for growth models in the MBE universality class, the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady-state regimes. For the MBE universality class, the positive and negative persistence exponents in the steady-state are found to be $theta^S_{+} = 0.66 pm 0.02$ and $theta^S_{-} = 0.78 pm 0.02$, respectively, in (1+1) dimensions, and $theta^S_{+} = 0.76 pm 0.02$ and $theta^S_{-} =0.85 pm 0.02$, respectively, in (2+1) dimensions. The noise reduction technique is applied on some of the (1+1)-dimensional models in order to obtain accurate values of the persistence exponents. We show analytically that a relation between the steady-state persistence exponent and the dynamic growth exponent, found earlier to be valid for linear models, should be satisfied by the smaller of the two steady-state persistence exponents in the nonlinear models. Our numerical results for the persistence exponents are consistent with this prediction. We also find that the steady-state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state. The dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form.
Numerical and analytic results for the exponent theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by the dynamic roughness exponent beta, with 0 < beta < 1; for beta = 1/2 the time evolution is Markovian. Using simulations of solid-on-solid models, of the discretized continuum equations as well as of the associated zero-dimensional stationary Gaussian process, we address two problems: The return of an initially flat interface, and the return to an initial state with fully developed steady state roughness. The two problems are shown to be governed by different exponents. For the steady state case we point out the equivalence to fractional Brownian motion, which has a return exponent theta_S = 1 - beta. The exponent theta_0 for the flat initial condition appears to be nontrivial. We prove that theta_0 to infty for beta to 0, theta_0 geq theta_S for beta < 1/2 and theta_0 leq theta_S for beta > 1/2, and calculate theta_{0,S} perturbatively to first order in an expansion around the Markovian case beta = 1/2. Using the exact result theta_S = 1 - beta, accurate upper and lower bounds on theta_0 can be derived which show, in particular, that theta_0 geq (1 - beta)^2/beta for small beta.
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