Molecular Dynamics simulation of a polymer chain translocating through a nanoscopic pore

The detection of linear polymers translocating through a nanoscopic pore is a promising idea for the development of new DNA analysis techniques. However, the physics of constrained macromolecules and the fluid that surrounds them at the nanoscopic scale is still not well understood. In fact, many theoretical models of polymer translocation neglect both excluded-volume and hydrodynamic effects. We use Molecular Dynamics simulations with explicit solvent to study the impact of hydrodynamic interactions on the translocation time of a polymer. The translocation time τ that we examine is the unbiased (no charge on the chain and no driving force) escape time of a polymer that is initially placed halfway through a pore perforated in a monolayer wall. In particular, we look at the effect of increasing the pore radius when only a small number of fluid particles can be located in the pore as the polymer undergoes translocation, and we compare our results to the theoretical predictions of Chuang et al. (Phys. Rev. E 65, 011802 (2001)). We observe that the scaling of the translocation time varies from τ ∼ N ^11/5 to τ ∼ N ^9/5 as the pore size increases (N is the number of monomers that goes up to 31 monomers). However, the scaling of the polymer relaxation time remains consistent with the 9/5 power law for all pore radii.     

Apparent correlations between the static length of relaxation and the linear size of dynamic heterogeneity in fragile liquids

The most puzzling aspect of the glass transition observed in laboratory is the decoupling of the dynamics from the structure. As an attempt to reconcile the dynamic and the static lengthscales associated with the glass problem, we discuss the apparent correlations between the static relaxation length, defined as that lengthscale over which the potential energy fluctuation is correlated, with the linear size of the dynamic heterogeneity. The dynamic heterogeneous domains with long life-times, may therefore be linked to the droplets of low potential energy, or the tightly bound regions inside the liquid.     

Dielectric relaxation of poly(ethylenglycol)- b-poly(propylenglycol)-b-poly(ethylenglycol) copolymers above the glass transition temperature

The complex dielectric permittivity has been measured for three poly(ethylenglycol)-b-poly(propylenglycol)-b-poly(ethylenglycol) copolymers with different content of poly(ethylenglycol) (15%, 33% and 80%), and increasing degree of crystallinity (0%, 10% and 20%, respectively). Only the non-crystalline sample shows the normal mode relaxation together with the segmental (α-relaxation) and the Johari-Goldstein (β-relaxation) modes. The crystalline samples show also polarization contributions due to the existence of interfaces between the crystallites and the amorphous phase. The relaxation times of the (α and normal modes can be described by a VFT equation with the same value of T₀. There is a slowing-down of the segmental mode due to the presence of crystallites. The temperature dependence of the α and β relaxations in the copolymers is very similar to that found in pure PPG, while there are significant differences in the case of the normal mode of the non-crystalline sample. The size of the cooperatively rearranging regions CRR, and the width of the glass transition region increase slightly with the degree of crystallinity. The temperature dependence of the size of CRRs is compatible with the prediction of fluctuation theory. No systematic effect of the degree of crystallinity on the β-relaxation has been found. Near T _g the β-relaxation time is close to the primitive time of the coupling model. Received: 31 May 2000     

Glass transition line for the system of charged hard spheres

We locate the glass transition line of the charged-hard-sphere system in the density-temperature plane, using a mean-field hypernetted chain approximation within the replica-symmetry-breaking scenario [S. Franz and G. Parisi, Phys. Rev. Lett. 79 (1997) 2486. [11]]. Our results demonstrate a dominant role of the steric factor and explain the ineffectiveness of purely Coulombic interactions in driving phase transitions.     

Dynamic-mechanical and nuclear magnetic resonance study of relaxation processes in ultra-high molecular weight polyethylene fibres

The relaxation processes (α, β, and γ) in UHMW PE fibres drawn to different draw ratios λ have been studied by dynamic-mechanical and nuclear magnetic resonance methods. The temperature dependences of tensile loss moduli E″ and spin-lattice relaxation times T ₁ have been analyzed assuming distribution of correlation times τ according to the Davidson—Cole function. The activation energies E _a and parameters ε characterizing widths of distribution, and asymptotic value τ ₀ for correlation times have been determined from experimental data for low-temperature γ-process and for high-temperature α-process. A weak β-process has been found by dynamic-mechanical method and quantitative analysis was made only for fibres with λ = 9. The temperature dependences of second moment M ₂ of the broad-line NMR spectra have been analyzed according to the Gutowsky—Pake formula, which includes only a single correlation time τ _c without distribution. In this case the activation energies E _a and values of τ ₀ have been determined.     

Overlap properties and adsorption transition of two Hamiltonian paths

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems. Received 4 December 1998 and Received in final form 10 March 1999     

Effect of counterions on the swelling of spherical polyelectrolyte brushes

We investigate the swelling of colloidal spherical polyelectrolyte brushes in the presence of different counterions. The colloidal particles consist of a solid poly(styrene) core of ca. 100 nm diameter onto which linear polyelectrolyte chains are chemically grafted. Two types of polyelectrolyte chains have been used here: The cationic polyelectrolyte poly(2-(acryloyl)ethyltrimethylammonium chloride)) (PATAC) and the anionic poly(styrenesulfonate) (PSS). Both systems are dispersed in water and the degree of swelling of the surface layer is studied by dynamic light scattering. Adding more and more salt leads to a strong shrinking of the surface layer as expected for polyelectrolyte brushes. It is shown that data obtained at low ionic strength can be collapsed on suitable master curves for monovalent and divalent counterions, respectively. For some ions, however, high salt concentrations may lead to a re-swelling of the brush layer in case of the cationic systems. This points to specific interactions of the counterions with the PATAC chains. This strong specific interaction between the counterions and the attached polyelectrolyte may even lead to flocculation of the particles at intermediate salt concentration. Surprisingly, for iodide and magnesium counterions the solubility increases again if the salt concentration is raised to 1 mol/l. Hence, specific interaction leads to salting-out effects as well as to salting-in effects for these colloidal particles. All specific effects seen at high concentrations of added salt can be explained by the increase of the reduced excluded-volume parameter which is due to the adsorption of salt ions.     

Molecular dynamics in thin films of isotactic poly(methyl methacrylate)

The molecular dynamics in thin films (18 nm-137 nm) of isotactic poly(methyl methacrylate) (i-PMMA) of two molecular weights embedded between aluminium electrodes are measured by means of dielectric spectroscopy in the frequency range from 50 mHz to 10 MHz at temperatures between 273 K and 392 K. The observed dynamics is characterized by two relaxation processes: the dynamic glass transition (α-relaxation) and a (local) secondary β-relaxation. While the latter does not depend on the dimensions of the sample, the dynamic glass transition becomes faster (≤2 decades) with decreasing film thickness. This results in a shift of the glass transition temperature T _g to lower values compared to the bulk. With decreasing film thickness a broadening of the relaxation time distribution and a decrease of the dielectric strength is observed for the α-relaxation. This enables to deduce a model based on immobilized boundary layers and on a region displaying a dynamics faster than in the bulk. Additionally, T _g was determined by temperature-dependent ellipsometric measurements of the thickness of films prepared on silica. These measurements yield a gradual increase of T _g with decreasing film thickness. The findings concerning the different thickness dependences of T _g are explained by changes of the interaction between the polymer and the substrates. A quantitative analysis of the T _g shifts incorporates recently developed models to describe the glass transition in thin polymer films. Received 12 August 2001 and Received in final form 16 November 2001     

Molecular-weight dependence of the glass transition temperature of freely-standing poly(methyl methacrylate) films

We have used transmission ellipsometry to measure the glass transition temperature, T_g, of freely-standing films of atactic and syndiotactic poly(methyl methacrylate) (PMMA). We have prepared films with different molecular weights, MW, (159×10³ < M _w < 1.3×10⁶) and film thicknesses, h, ( 30nm < h < 200 nm). For the high-MW ( M _w > 509×10³) atactic PMMA films, we find that T_g decreases linearly with decreasing h, which is qualitatively similar to previous results obtained for high-MW freely-standing polystyrene (PS) films. However, the overall magnitude of the T_g reduction is much less (by roughly a factor of three) for the high-MW freely-standing PMMA films than for freely-standing PS films of comparable MW and h. The observed differences between the freely-standing PMMA and PS film data suggest that differences in chemical structure determine the magnitude of the T_g reduction and we discuss the possible origins of these differences. Our analysis of the MW-dependence of the T_g reductions suggests that the mechanism responsible for the MW-dependent T_g reductions observed in the high-MW freely-standing films is different than that responsible for the MW-independent T_g reductions observed in the low-MW freely-standing and supported films.     

Scattering properties of gradient heteropolymers obtained by “living” free-radical copolymerization

An original, quantitative, theory of “living” radical copolymerization has been developed proceeding from the current concepts of its kinetics and mechanism. This theory enables one to calculate both the dependence of monomers' conversion on time and any statistical characteristics of the chemical structures of the copolymers formed. Expressions have been derived describing the angular dependence of the scattering amplitude of the copolymerization products. The results of quantitative calculations of these characteristics have been also presented to exemplify the potentialities of the theory. Received 13 February 2001 and Received in final form 4 February 2002     

Molecular dynamics in nanophase-separated comb-like poly( $ \upalpha$- n-alkyl $ \upbeta$-L-aspartate)s

A series of poly( -n-alkyl -L-aspartates) which are nanophase self-assembled comb-like polymers has been studied by dielectric spectroscopy in a broad frequency range ( 10^-23×10⁶ Hz), with n-alkyls side chains of various lengths, 10n18. In every member of the series the same relaxations were identified after the decomposition of the experimental isothermal trace in up to three peaks with relaxation times distributions. The strength, width and average relaxation time for all the relaxation modes were determined for each material. Besides the local low temperature, Arrhenius modes, two relaxation modes, and , present a cooperative character whose dynamics are not affected by the side chains melting. The relaxation is a polyethylene-like glass transition of the amorphous side chains and its dynamics is strongly dependent on the n value due to the increasing restrictions imposed by the self-assembled confinement. The strength of the relaxation mode increases as the lateral chains loose their 2D order. The restricted chopstick motion of the rigid rods is thought to be the origin of the mode; this motion is hindered at temperatures where the cage size decreases as a result of the increasing disorder with temperature.     

Ground state and glass transition of the RNA secondary structure

RNA molecules form a sequence-specific self-pairing pattern at low temperatures. We analyze this problem using a random pairing energy model as well as a random sequence model that includes a base stacking energy in favor of helix propagation. The free energy cost for separating a chain into two equal halves offers a quantitative measure of sequence specific pairing. In the low temperature glass phase, this quantity grows quadratically with the logarithm of the chain length, but it switches to a linear behavior of entropic origin in the high temperature molten phase. Transition between the two phases is continuous, with characteristics that resemble those of a disordered elastic manifold in two dimensions. For designed sequences, however, a power-law distribution of pairing energies on a coarse-grained level may be more appropriate. Extreme value statistics arguments then predict a power-law growth of the free energy cost to break a chain, in agreement with numerical simulations. Interestingly, the distribution of pairing distances in the ground state secondary structure follows a remarkable power-law with an exponent -4/3, independent of the specific assumptions for the base pairing energies.     

Effect of physical ageing in thin glassy polymer films

We have studied the effect of physical ageing in thin supported glassy polystyrene films by using ellipsometry to detect overshooting in the expansivity-temperature curve upon heating of aged samples. Films with thickness 10-200 nm have been aged at 70^° C and 80^° C (below the bulk glass transition temperature). We observe clear relaxation peaks in the expansivity-temperature curve for films thicker than 18 nm but not for the 10 nm film. The intensity of the relaxation peak is inversely proportional to the film thickness, while the temperatures characteristic to the relaxation peak are almost independent of the film thickness. These observations are successfully interpreted by the idea that the surface layer of the order of 10 nm has liquid-like thermal properties. Received 28 October 2002 / Published online: 1 April 2003 RID="a" ID="a"Present address: Yokohama Research Center, Mitsubishi Chemical Corporation, 1000 Kamoshida-chou, Aoba-ku, Yokohama 227-8502, Japan; e-mail: kawana@rc.m-kagaku.co.jp     

Analysis of polymer adsorption onto colloidal particles

The structure of the layer formed after polymer adsorption onto a spherical particle is numerically studied by means of the application of the Single-Chain Mean-Field theory. We have determined several overall layer properties including the monomer volume fraction profiles, the layer thickness, adsorbances related to loops and to tails, as well as the variation of the crossover distance between loops and tails for different particle radii and fixed polymer length. When the radius of the sphere is small enough to affect the loop layer, one enters a single-adsorbed-chain regime, characterized by a critical sphere radius. In this regime, structural changes in the adsorbed layer arise. For such small sphere, the loop layer is confined to a region whose thickness is of the order of the radius of the adsorbing sphere, and two long tails dominate the outer layer and the adsorbance due to tails dominates that due to loops. An analysis of the structure of the outer tail layer for this small sphere case is also presented.     

Specific heats of the charge density wave compounds o-TaS and (TaSe ) I

Specific heats of the charge-density-wave compounds o-TaS₃ and (TaSe₄)₂I have been measured over the wide temperature interval 10 K-300 K. Both systems exhibit strong non-Debye behavior. Very weak and broad anomalies are observed at the Peierls transition temperatures. For o-TaS₃, the change in the curvature of the specific heat occurs at temperature of 40 K where glass transition has been deduced from dielectric measurements, and an extended scaling analysis suggests that the glass transition is associated with a dynamical cross over in length scales. We briefly discuss the characteristics and physical origins of the anomalies at both the Peierls and glass transitions. Received 5 April 2002 / Received in final form 28 June 2002 Published online 17 September 2002     

The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

The absence of physical aging effects on the relaxation of rubbing-induced birefringence in polystyrene

We found, through extensive experimental studies, that the physical aging effects are absent in the relaxation of rubbing-induced birefringence (RIB) in polystyrene (PS), and the relaxation involves very small length scale. A phenomenological model based on individual birefringence elements is proposed for the RIB relaxation. The relaxation times (RTs) of the elements are found to be independent of the thermal or stress history of the samples, either before or after the formation of the birefringence. The RTs are also independent of the molecular weight, rubbing conditions, and film thickness, while the RTs distribution function does depend on the molecular weight and rubbing conditions. The model provides quantitative interpretations that agree very well with all the reported experimental results, and sheds important light on the novel behaviors of the RIB relaxation. The absence of physical aging effects is probably due to the combined effects of small length scale of the RIB relaxation, and the accelerated aging speed in the near surface region in which the RIB concentrates.     

Growth exponent in the Domany-Kinzel cellular automaton

Dynamic heterogeneities, i.e. the presence of molecules with different mobilities, have been established as one of the key features of the physics of supercooled liquids. Here we study in detail how the mobility of an individual molecule fluctuates with time. Our analysis is based on a time series of molecular dynamics simulations for a low molecular weight glass-former, propylene carbonate. We find that the variation of mobility with time of initially slow molecules significantly differs from that of initially fast molecules. We explicitly show the relation to the rate memory parameter which recently has been introduced to quantify the mobility fluctuations as observed via multidimensional NMR experiments. In this way qualitative agreement between simulation and experiment can be established although the time scales of simulation and NMR experiment differ by many orders of magnitude. Received 10 April 2000 and Received in final form 21 September 2000