Mean Square Radius Research Articles

Monte Carlo simulation of a single ring among linear chains: Structural and dynamic heterogeneity

We perform lattice Monte Carlo simulation using the bond-fluctuation model to examine the conformation and dynamic properties of a single small flexible ring polymer in the matrix of linear chains as functions of the degree of polymerization of the linear chains. The average conformation properties as gauged by the mean-square radius of gyration and asphericity parameter are insensitive to the chain length for all the chain lengths examined (30, 100, 300, and 1000). However, in the longer chain (300 and 1000) samples, there is an increased spread in the distribution of the value of these quantities, suggesting structural heterogeneity. The center-of-mass diffusion of the ring shows a rapid decrease with increasing chain length followed by a more gradual change for the two longer chain systems. In these longer chain systems, a wide spread in the value of the apparent self-diffusion coefficient is also observed, as well as qualitatively different square displacement trajectories among the different samples, suggesting heterogeneity in the dynamics. A primitive path analysis reveals that in these long chain systems, the ring can exist in topologically distinct states with respect to threading by the linear chains. Threading by the linear chain can dramatically slow down and in some cases stall the diffusive motion of the ring. We argue that the life times for these topological conformers can be longer than the disentanglement time of the linear chain matrix, so that the ring exhibits nonergodic behavior on time scales less or comparable to the life time of these conformers. Our results suggest a picture of the ring diffusion as one where the diffusion path consists of distinctive segments, each corresponding to a different conformer, with slow interconversion between the different conformers.

Effect of spin-orbit nuclear charge density corrections due to the anomalous magnetic moment on halonuclei

In this paper we consider the contribution of the anomalous magnetic moments of protons and neutrons to the nuclear charge density. We show that the spin-orbit contribution to the mean-square charge radius, which has been neglected in recent nuclear calculations, can be important in light halonuclei. We estimate the size of the effect in helium, lithium, and beryllium nuclei. It is found that the spin-orbit contribution represents a $~2%$ correction to the charge density at the center of the $^{7}\mathrm{Be}$ nucleus. We derive a simple expression for the correction to the mean-square charge radius due to the spin-orbit term and find that in light halonuclei it may be larger than the Darwin-Foldy term and comparable to finite size corrections. A comparison of experimental and theoretical mean-square radii including the spin-orbit contribution is presented.

A steered molecular dynamics simulation on the elastic behavior of adsorbed star polymer chains

Elastic behavior of 4-branched star polymer chain with different chain length N adsorbed on attractive surface is investigated using steered molecular dynamics (SMD) simulation method based on the united-atom (UA) model for branched alkanes. The simulation is realized by pulling up the chain via a linear spring with a constant velocity v = 0.005 nm/ps. At the beginning, the chain lies extensionally on adsorbed surface and suffers continuous deformations during the tensile process. Statistical parameters as mean-square radii of gyration xy, z, shape factor , describing the conformational changes, sectional density which gives the states of the chain, and average surface attractive energy , average total energy , average force probed by the spring, which characterize the thermodynamic properties, are calculated in the stimulant process. Remarkably, distinguishing from the case in linear chains that there only exists one long plateau in the curve of , the force plateau in our study for star chains is multiple, denoting different steps of desorption, and this agrees well with the experimental results in essence. We find during the tensile process, there are three characteristic distances Zc, Zt and Z0 from the attractive surface, and these values vary with N. When Z = Zc, the chain is stripped from the surface, but due to the form of wall-monomer interaction, the surface retains weak influence on the chain till Z = Zc. From Z = Zt, parameters , and respectively reach a stable value, while the shape and the size of the chain still need adjustments after Zt till Z0 to reach their equilibrium states. Specifically, for short chain of N = 41, Zt and Z0 are incorporated. These results may help us to deepen the knowledge about the elastic behavior of adsorbed star polymer chains.

A Monte Carlo study of the second virial coefficient of semiflexible ring polymers

A Monte Carlo (MC) study was made of the second virial coefficient A2 of the ideal Kratky–Porod (KP) worm-like ring using a model composed of infinitely thin bonds with harmonic bending energy between successive bonds. Two kinds of statistical ensembles were generated: one composed of configurations of all kinds of knots with the Boltzmann weight, called the mixed ensemble, and the other composed of only those of the trivial knot, called the trivial-knot ensemble. The effective volume VE excluded to one ring by the presence of another, resulting only from a topological interaction, and also the mean-square radius of gyration 〈S2〉 were evaluated for each ensemble. The dimensionless quantity λVE/L2 proportional to A2 was found to be a function only of the reduced total contour length λL, as in the case of λ〈S2〉/L, where λ−1 is the stiffness parameter of the KP ring and L is its total contour length. The quantity λVE/L2 first increased and then decreased after passing through a maximum at λL≃5, as λL was increased. A comparison with literature data for ring atactic polystyrene in cyclohexane at Θ shows that the present MC results may qualitatively explain the behavior of the data. The effective volume VE excluded to a Kratky–Porod (KP) worm-like ring by the presence of another, resulting only from a topological interaction, was evaluated by Monte Carlo simulations. The quantity λVE/L2 proportional to the second virial coefficient A2 was shown to be a function only of λL with λ−1 the stiffness parameter of the KP ring and L its total contour length.

Rigorous derivation of the perimeter generating function for the mean-squared radius of gyration of convex polygons

We have rigorously derived the perimeter generating function for the mean-squared radius of gyration of convex polygons. This function was first conjectured by Jensen. His nonrigorous result is based on the analysis of the long series expansions.

DIMENSION AND DIPOLE MOMENT OF POLY(TETRAFLUOROETHYLENE) AND POLY(DIMETHYLSILYLENE) CHAINS

A study of the mean-square radius of gyration and mean-square dipole moment of the symmetric disubstituted polymers is presented basing on the improved rotational-isomeric-state method. The deduced formulas are used to investigate the conformation-dependent properties of poly( tetrafluoroethylene) ( PTFE), poly(dimethylsilylene) ( PDMS) and polyethylene ( PE) chains. Here,the configuration parameters of the PTFE4 (PTFE of the 4-state model) chain and PDMS chain are calculated to be about 0. 44 ·mol0. 5·g -0. 5 and 0. 43 ·mol0. 5·g -0. 5 respectively for large polymerization degree x. However,the temperature coefficient of PDMS chain-7. 32 × 10 -3 K -1 is different obviously from that of PTFE and PE chains (about- 1. 00 × 10-3 K -1). The calculated characteristic ratios of mean-square dipole moment for long PTFE and PDMS chains are rather small,such as the ratio of PDMS is 0. 27. The results show that PTFE and PDMS are non-polar polymers,good dielectric and poor in induction,even though the dipole moments of C—F and Si—C are large in PTFE and PDMS chains. Therefore,the polar and dielectric properties of polymers are also affected by the conformation and structure of chains. In addition,the chain end effect of short PTFE and PDMS chains (repeat unit x 10) results in obvious change of the ratios with x,which is in agreement with the results of Flory et al.

On the possibilities for studying the electromagnetic properties of monoenergetic solar neutrinos in the borexino experiments

Electroweak (EW) and electromagnetic (EM) scattering of solar beryllium neutrinos by electrons are analyzed. An analysis of the influence of the mean-square charge radius of an electron neutrino $$ r_{\nu _e } = \sqrt {\left\langle {r_{_{\nu _e } }^2 } \right\rangle } $$ on differential and total cross sections is performed. The possibility of measuring the magnetic moment of an electron neutrino (μv) on the basis of isolating its contribution to the section of the discussed processes is considered.

Resonant recombination at ion storage rings: a conceptual alternative for isotope shift and hyperfine studies

Sharp resonant structures in the cross section of the atomic electron-ion collision process of dielectronic recombination are exploited to study isotope shifts and hyperfine interaction of heavy highly-charged ions. This novel approach provides a conceptual alternative to existing methods. In this contribution, we present a series of measurements, which we performed at the heavy ion storage ring ESR of the GSI Helmholtzzentrum fur Schwerionenforschung, Darmstadt, Germany. In a first experiment the stable isotopes A = 142 and A = 150 of three-electron neodymium ANd57 + were studied. Isotope shifts of dielectronic resonances associated with 2s − 2pj (j = 1/2, 3/2) transitions were extracted from the measured data. The evaluation of the energy shift was performed within a full QED framework and yielded a change in the mean-square charge radius of \(^{142,150}\delta \langle r^2 \rangle = -1.36(1)(3)\) fm2. At GSI, in addition to the investigation of stable isotopes unstable species can be artificially synthesized and studied. Radioisotopes produced in-flight from fragmentation of a 238U primary beam were injected into the ESR and were subsequently separated by their mass-to-charge ratio. This enabled us to perform first DR experiments with the exotic nuclei 237U89 + (Z = 92 )and 234Pa88 + (Z = 91).

Quantum Monte Carlo study of large spin-polarized tritium clusters

This work expands recent investigations in the field of spin-polarized tritium (T downward arrow) clusters. We report the results for the ground-state energy and structural properties of large T downward arrow clusters consisting of up to 320 atoms. All calculations have been performed with variational and diffusion Monte Carlo methods, using an accurate ab initio interatomic potential. Our results for N < or = 40 are in good agreement with results obtained by other groups. Using a liquid-drop expression for the energy per particle, we estimate the liquid equilibrium density, which is in good agreement with our recently obtained results for bulk T downward arrow. In addition, the calculations of the energy for large clusters have allowed for an estimation of the surface tension. From the mean-square radius of the drop, determined using unbiased estimators, we determine the dependence of the radii on the size of the cluster and extract the unit radius of the T downward arrow liquid.

ELASTIC BEHAVIOR OF POLYMER CHAINS CONFINED IN PARALLEL INTERFACES

The elastic behaviors of star and linear polymer chains confined in parallel interfaces are investigated using pruned-enriched-rosenbluth method (PERM) based on the self-avoiding walk (SAW) model.The simulation results suggest that if the interfaces have the adsorptive effect on the chains,the accretion of the distance between parallel interfaces D needs acting force; while if the interfaces have no attraction,the accretion of D is a spontaneous process. In our simulation,we calculate the changes of the mean-square radii of gyration 〈S2〉 and the shape factor 〈δ〉 with D,describing the changes of dimension and shape of the star and linear chains.Additionally,in order to understand the structure and the mechanical behavior in more detail,we also study confined chains of different structure such as train,loop,bridge and tail chains.

Isotope shifts in dielectronic recombination: From stable to in-flight-produced nuclei

The study of isotope shifts and hyperfine effects in dielectronic recombination (DR) resonance spectra strikes a conceptually new path for investigations of nuclear properties such as charge radius, spin, magnetic moment of nuclei or lifetimes of long-lived excited nuclear states. A series of DR experiments with heavy three-electron ions (Li-like) was performed at the heavy-ion storage ring ESR of the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany. In a pilot experiment the two stable isotopes A=142 and A=150 of neodymium ANd57+ were investigated. From the displacement of DR resonances the isotope shifts δE142,150(2s – 2Pl/2) = 40.2(3)(6) meV and δE142,150(2s – 2p3/2) = 42.3(12)(20) meV for 2s – 2Pj transitions of the Li-like ions have been obtained. An evaluation within a full QED framework yielded a change in the mean-square charge radius of 142,150δ(r2) = −1.36(1)(3) fm2. At GSI, in addition to stable isotopes, in-flight synthesized radioisotopes can be studied as well. The production of radioisotopes of interest, the subsequent separation in the storage ring ESR and first DR experiments with the exotic nuclei 237U89+ and 234Pa88+ (Z=91) are presented. The paper is concluded with a brief outlook at future DR experiments with heavy radioisotopes at the ESR.

Conformational, Dimensional, and Hydrodynamic Properties of Amylose Tris(n-butylcarbamate) in Tetrahydrofuran, Methanol, and Their Mixtures

Twelve amylose tris(n-butylcarbamate) (ATBC) samples ranging in weight-average molecular weight from 1.7 × 104 to 1.7 × 106 have been prepared and studied by light and small-angle X-ray scattering, sedimentation equilibrium, viscosity, infrared absorption (IR), and optical rotation in methanol (MeOH), tetrahydrofuran (THF), and their mixtures at 25 °C (or 20−25 °C for IR). Data for the mean-square radius of gyration, the particle scattering function, and the intrinsic viscosity are analyzed on the basis of the wormlike chain to yield h (contour length per residue) = 0.32 nm and λ−1 (Kuhn’s segment length) = 11 nm in MeOH and h = 0.26 nm and λ−1 = 75 nm in THF. The high stiffness in THF indicated by λ−1 = 75 nm is most likely due to the intramolecular hydrogen bonding (between C═O and NH groups of ATBC) observed as the splitting amide I band in the IR spectra. Furthermore, the h value in this solvent is considerably smaller than the helix pitches per residue of 0.37−0.40 nm for amylose triesters in the crystalline state and those of 0.32−0.42 nm for semiflexible amylose tris(phenylcarbamate) in various solvents (λ−1 = 15−24 nm), indicating that the ATBC chain forms a tightly wound helix in THF. As the number of intramolecular hydrogen bonds decreases, i.e., as the MeOH content increases in THF−MeOH mixed solvents, λ−1 decreases while h increases. These relationships are successfully explained by a two-state model in which each chain consists of randomly distributed semiflexible (loosely helical) and rodlike (rigid helical) sequences. The resultant h values for the rodlike and semiflexible portions are 0.25−0.26 and 0.32 nm, respectively.

Chain dimension of polystyrene-like hyperbranched polymers with various chain end groups in THF

A hyperbranched polymer (HPS-DC) synthesized using N,N-diethylamino -dithiocarbamoylstyrene as an inimer and a hyperbranched poly(4-methylstyrene) (HPS-H) prepared by hydrogenation of the HPS-DC are characterized in tetrahydrofuran (THF) solutions by static and dynamic light scattering measurements. The experimental values of z-averaged mean-square radius of gyration (<S2>z1/2) and hydrodynamic radius (RH) of the HPS-H have smaller dimensions than those of the linear polystyrene (PS) at the same degree of polymerization (Nw), whereas the RH of the HPS-DC in the region of Nw < 700 is larger than that of the linear PS at the same Nw. The Nw-dependence of <S2>z1/2 and RH for the HPS-H are described by a randomly trifunctional branched polymer model with the molecular weight per a branch point (4.55 × 103 g/mol) and the chain dimensions of the linear PS in THF at 25 °C.

Critical examination of isotope shift and fine structure measurements for optical transitions in 6,7LiThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008.

Precise isotope shift and fine structure measurements are critically reviewed. Each experiment was checked for whether the data found for different transitions yielded consistent values for the difference in mean-square nuclear charge radius Δr2 of 6,7Li. Experiments that passed this test found Δr2 = 0.735 ± 0.036, 0.755 ± 0.023, and 0.739 ± 0.013 fm2 by studying the Li+ 1s2s 3S→1s2p 3P transition, the Li D lines and the Li 2S1/2→3S1/2 transition, respectively. These data determine the difference in mean-square nuclear charge radius 25 times more accurately than electron scattering. Similarly, averaging the fine structure data from the same experiments gives 62 678.75 ± 0.55 MHz for the 7Li+ 1s2p 3P1–2 interval, in good agreement with theory. The results for the 6,7Li 2P fine structure intervals, 10 0.52.954 ± 0.049 and 10 053.154 ± 0.040 MHz, exceed computed values by 2 MHz and yield a splitting isotope shift, which is nearly a factor of 2 lower than a theoretical estimate.

Frequency-comb-based measurements of lithium and beryllium isotopes for nuclear structure studiesThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008.

We report on the measurement of the 2s-3s transition frequencies in the stable lithium isotopes and 2s-2p isotope shift measurements of 7,9,10,11Be, using a femtosecond frequency comb. For the beryllium isotopes, we extract the changes in the mean-square nuclear charge radius along the isotope chain by comparison with high-precision atomic mass shift calculations. The 2s-3s transition frequency is compared with theoretical calculations, and possibilities to extract an absolute value for the nuclear charge radius of lithium isotopes are discussed.

Collapse-driven self-assembly of multiblock chains: A Monte Carlooff-lattice study

Abstract We perform off-lattice Monte Carlo simulations for multiblock chains, ( 5 A - 5 B ) n , with n = 10 , 20 , 30 , 40 , 50 , and 60 , in an implicit selective solvent, using a discontinuous square-well potential. We present selected thermodynamic and structural properties as a function of the reduced temperature, such as the reduced energy per segment, the reduced heat capacity, and the mean-squared radius of gyration. We observe that the collapse-driven self-assembled structure is not spherical above certain value of chain length, N, and develops a non-spherical globular structure with multiple cores.

Laser Spectroscopy of Niobium Fission Fragments: First Use of Optical Pumping in an Ion Beam Cooler Buncher

A new method of optical pumping in an ion beam cooler buncher has been developed to selectively enhance ionic metastable state populations. The technique permits the study of elements previously inaccessible to laser spectroscopy and has been applied here to the study of Nb. Model independent mean-square charge radii and nuclear moments have been studied for ;{90,90 m,91,91 m,92,93,99,101,103}Nb to cover the region of the N=50 shell closure and N approximately 60 sudden onset of deformation. The increase in mean-square charge radius is observed to be less than that for Y, with a substantial degree of beta softness observed before and after N=60.

Solvent‐dependent conformation of amylose tris(phenylcarbamate) as deduced from scattering and viscosity data

The z-average mean-square radius of gyration S(2)(z), the particle scattering function P(k), the second virial coefficient, and the intrinsic viscosity [eta] have been determined for amylose tris(phenylcarbamate) (ATPC) in methyl acetate (MEA) at 25 degrees C, in ethyl acetate (EA) at 33 degrees C, and in 4-methyl-2-pentanone (MIBK) at 25 degrees C by light and small-angle X-ray scattering and viscometry as functions of the weight-average molecular weight in a range from 2 x 10(4) to 3 x 10(6). The first two solvents attain the theta state, whereas the last one is a good solvent for the amylose derivative. Analysis of the S(2)(z), P(k), and [eta] data based on the wormlike chain yields h (the contour length or helix pitch per repeating unit) = 0.37 +/- 0.02 and lambda(-1) (the Kuhn segment length) = 15 +/- 2 nm in MEA, h = 0.39 +/- 0.02 and lambda(-1) = 17 +/- 2 nm in EA, and h = 0.42 +/- 0.02 nm and lambda(-1) = 24 +/- 2 nm in MIBK. These h values, comparable with the helix pitches (0.37-0.40 nm) per residue of amylose triesters in the crystalline state, are somewhat larger than the previously determined h of 0.33 +/- 0.02 nm for ATPC in 1,4-dioxane and 2-ethoxyethanol, in which intramolecular hydrogen bonds are formed between the C==O and NH groups of the neighbor repeating units. The slightly extended helices of ATPC in the ketone and ester solvents are most likely due to the replacement of those hydrogen bonds by intermolecular hydrogen bonds between the NH groups of the polymer and the carbonyl groups of the solvent.

Shapes of Two-Dimensional Excluded Volume Continuum Star Polymers

The shapes of excluded volume, two-dimensional star polymers are explored with the renormalization group and Monte Carlo computer simulation of a tangent hard disk model. The mean-square radius of gyration, the g-ratio, and the asphericity of linear and star polymers are examined. The standard ϵ expansion for the g-ratio is modified to use the known value of the radius of gyration expansion exponent rather than only the first-order expansion value. Good agreement is obtained with the current Monte Carlo Pivot algorithm results and previous simulations of other polymer models. Our approach also improves the predictions of the g-ratio in three dimensions, significantly enhancing the accuracy of the renormalization group for calculating shape properties.

A NEW DIAGNOSTIC METHOD FOR ASSESSMENT OF STELLAR STRATIFICATION IN STAR CLUSTERS

We propose a new method for the characterization of stellar stratification in stellar systems. The method uses the mean-square radius (also called the Spitzer radius) of the system as a diagnostic tool. An estimate of the observable counterpart of this radius for stars of different magnitude ranges is used as the effective radius of each stellar species in a star cluster. We explore the dependence of these radii on magnitude as a possible indication of stellar stratification. This method is the first of its kind to use a dynamically stable radius, and though seemingly trivial it has never been applied before. We test the proposed method using model star clusters, which are constructed to be segregated on the basis of a Monte Carlo technique, and on Hubble Space Telescope observations of mass-segregated star clusters in order to explore the limitations of the method in relation to actual data. We conclude that the method performs efficiently in the detection of stellar stratification and its results do not depend on the data, provided that incompleteness has been accurately measured and the contamination by the field population has been thoroughly removed. Our diagnosis method is also independent of any model or theoretical prediction, in contrast to the `classical' methods used so far for the detection of mass segregation.