Viscoelastic study of the conformational transition of poly(methacrylic acid) in dilute aqueous solution

The dynamic viscosity of dilute aqueous solution of poly(methacrylic acid) (PMA) was measured over the frequency range 2–500 kHz for various degrees of ionization. The relaxation spectrum calculated from the viscosity exhibits a conformational relaxation spectrum in the short-time region and a rotational one in the long-time region. The former is fitted by the Zimm theory over the entire range of ionization, including the transition from a compact structure to an open one. The conformational relaxation time begins to increase at the midpoint of the transition region, but the rotational relaxation time increases very markedly in the initial stage of the transition. The present and previously reported experimental findings are interpreted in terms of the assumption that the compact structure is stabilized by short-range methyl–methyl bonding as well as “long-range” methyl–methyl bonding (bonding between methyl groups spatially close but remotely connected along the chain contour). In the initial stage of the transition, the latter primarily break up, resulting in expansion of overall chain dimensions, and subsequently the former are destroyed, resulting in the change in local chain conformation.     

Shear history independence in colloidal aggregation

Stimulated by experiments, we have carried out detailed simulations of aggregation in the presence of shear in a model colloidal system with a short-range attractive potential. For weak shear rates, we find that the shear enhanced the aggregation and that the long-time state of the system is independent of the shear history. For strong shear rates, precipitous fragmentation occurred after the shear was turned on and, after an induction period, the aggregation quickly rebounded in a stochastic manner similar to classical nucleation phenomena. However, the long-time state of the system is, once again, independent of the shear history. Thus, for both weak and strong shear cases, the shear rate acts as a state variable of the aggregating system. Shear rates employed in the simulations can be attained in laboratory experiments, as confirmed by computing the dimensionless Péclet numbers.     

Self-diffusion of rodlike and spherical particles in a matrix of charged colloidal spheres: a comparison between fluorescence recovery after photobleaching and fluorescence correlation spectroscopy

The fluorescence recovery after photobleaching (FRAP) method and the fluorescence correlation spectroscopy (FCS) have been applied on suspensions of highly charged colloidal spheres with a small content of rod-shaped tobacco mosaic virus (TMV) particles. Since these methods only determine the self-diffusion coefficient of the fluorescently labeled species, D(S) of the rods and the spheres could independently be measured. The ionic strength of the dispersion medium has been varied to measure self-diffusion of rods and spheres in dependence on the degree of order of the matrix spheres. In contrast to FRAP, which allows the determination of the long-time self-diffusion coefficient D(S) (L), FCS measures self-diffusion on a shorter time scale. Thus a comparison of the results that were obtained by FCS and FRAP, in combination with Brownian Dynamics simulations, gives insight into the time dependence of the self-diffusion coefficient of an interacting colloidal system. As the mean interparticle distance of the matrix is of the same order of magnitude as the length of a TMV rod, the rotational motion is influenced by the assembly of spheres around a TMV particle. Since FCS is sensitive both to translational and rotational motion, whereas FRAP, which probes the diffusion at much larger length scales, is only sensitive to the translational motion of TMV, the comparison of diffusion coefficients measured employing FRAP and FCS can give some insights in the rotational diffusion: the experimental data indicate a slowing down of the rotational motion of a TMV rod with increasing structural order of the matrix spheres.     

The role of axis embedding on rigid rotor decomposition analysis of variational rovibrational wave functions

Approximate rotational characterization of variational rovibrational wave functions via the rigid rotor decomposition (RRD) protocol is developed for Hamiltonians based on arbitrary sets of internal coordinates and axis embeddings. An efficient and general procedure is given that allows employing the Eckart embedding with arbitrary polyatomic Hamiltonians through a fully numerical approach. RRD tables formed by projecting rotational-vibrational wave functions into products of rigid-rotor basis functions and previously determined vibrational eigenstates yield rigid-rotor labels for rovibrational eigenstates by selecting the largest overlap. Embedding-dependent RRD analyses are performed, up to high energies and rotational excitations, for the H(2) (16)O isotopologue of the water molecule. Irrespective of the embedding chosen, the RRD procedure proves effective in providing unambiguous rotational assignments at low energies and J values. Rotational labeling of rovibrational states of H(2) (16)O proves to be increasingly difficult beyond about 10,000 cm(-1), close to the barrier to linearity of the water molecule. For medium energies and excitations the Eckart embedding yields the largest RRD coefficients, thus providing the largest number of unambiguous rotational labels.     

Morphology changes in the evolution of liquid two-layer films

We consider a thin film consisting of two layers of immiscible liquids on a solid horizontal (heated) substrate. Both the free liquid-liquid and the liquid-gas interface of such a bilayer liquid film may be unstable due to effective molecular interactions relevant for ultrathin layers below 100-nm thickness, or due to temperature-gradient-caused Marangoni flows in the heated case. Using a long-wave approximation, we derive coupled evolution equations for the interface profiles for the general nonisothermal situation allowing for slip at the substrate. Linear and nonlinear analyses of the short- and long-time film evolution are performed for isothermal ultrathin layers, taking into account destabilizing long-range and stabilizing short-range molecular interactions. It is shown that the initial instability can be of a varicose, zigzag, or mixed type. However, in the nonlinear stage of the evolution the mode type, and therefore the pattern morphology, can change via switching between two different branches of stationary solutions or via coarsening along a single branch.     

Anomalously slow solvent structural relaxation accompanying high-energy rotational relaxation

Experimental and theoretical work on the relaxation of rapidly rotating solutes in liquids have pointed out a number of striking features. Even in rapidly relaxing solvents, the relaxation proceeds quite slowly, exhibiting a manifestly nonlinear response that depends explicitly on the initial rotational energy. In this paper, we show how the long-time behavior, in particular, stems from a strong coupling of solute orientation to local solvent geometry. This coupling creates a rotational friction that decreases sharply with rotational energy, allowing for the protracted survival of not only high-angular-momentum rotational states but the cavity-like low-friction solvent geometries. We show, further, that the slow dynamics is dynamically heterogeneous. The distribution of excited rotors is marked by a distinct population of slowly relaxing hot rotational states. This population can be traced directly to the small subset of liquid configurations that happen to have low rotational friction values at the instant at which the rapid rotation started, indicating an unusual failure of the normally chaotic environment of a liquid to randomize initial conditions.     

Simulations of concentrated suspensions of rigid fibers: relationship between short-time diffusivities and the long-time rotational diffusion

Brownian dynamics simulations of the behavior of suspensions of fibers demonstrate that the scaling of the rotational diffusivity with respect to the number density (nL3) is a sensitive function of the thickness and the parameter L2D(R0)/D(T0), where D(R0) is the rotational diffusivity at infinite dilution, D(T0) is the average center-of-mass diffusivity at infinite dilution, and L is the fiber length. Existing theories for the long-time rotational diffusivities of rigid fibers in the semidilute and concentrated regimes fail to accurately account for the relationship with the dilute values of the rotational and translational diffusivities of the various physical models used to simulate the fibers. The concentration regime studied in this work ranges from a number density of nL3 approximately 0-150, which is below the transition from an isotropic to nematic state. The effect of the fiber thickness was studied by performing simulations of rods with aspect ratios (fiber length over diameter) of 25, 50, and 500, as well as performing projections for infinitely thin fibers. The excluded volume of the rods was enforced through the use of short-range potentials. For a rod with an aspect ratio of 50 with a parameter of L2D(R0)/D(T0)=9, which corresponds to a slender-body model of the individual fibers, the rotational diffusivity (D(R)) scales as D(R)/D(R0) approximately (nL3)(-1.9) in the concentration regime of 70 < or = nL3 < or = 150. Similarly with a parameter of L2D(R0)/D(T0)=4, corresponding to a rigid-dumbbell model, the rotational diffusivity scales as D(R)/D(R0) approximately (nL3)(-1.1) over the same range of concentrations. For rods with aspect ratios of 25, it is observed that a difference in the scaling is seen for L2D(R0)/D(T0) approximately < 8, with higher values of this ratio exhibiting essentially the same scaling. Additional values of the ratio L2D(R0)/D(T0) were investigated to determine the overall behavior of the suspension dynamics with respect to this parameter. These findings resolve discrepancies between simulation results for rotational diffusivities reported by previous investigators and provide new insights for the development of an accurate theory for the diffusivity of rigid rods suspended in solution.     

Picosecond rotational reorientation of cresyl violet in polymer solution

Picosecond absorption spectroscopy has been used to study the rotational reorientation of cresyi violet in methanol solutions containing poly(ethylene oxide). The increase in the rotational reorientation time with increasing polymer concentration can be attributed to the short-range hydrodynamic interactions between the dye and entangled polymer chains.     

Communication: translational Brownian motion for particles of arbitrary shape

A single Brownian particle of arbitrary shape is considered. The time-dependent translational mean square displacement W(t) of a reference point at this particle is evaluated from the Smoluchowski equation. It is shown that at times larger than the characteristic time scale of the rotational Brownian relaxation, the slope of W(t) becomes independent of the choice of a reference point. Moreover, it is proved that in the long-time limit, the slope of W(t) is determined uniquely by the trace of the translational-translational mobility matrix μ(tt) evaluated with respect to the hydrodynamic center of mobility. The result is applicable to dynamic light scattering measurements, which indeed are performed in the long-time limit.     

Computer simulations of diffusion and dynamics of short-chain polyelectrolytes

Brownian dynamics simulations are conducted to investigate the diffusional and dynamic properties of polyelectrolytes in dilute salt-free solutions. The polyelectrolyte molecule is represented by a bead-spring chain in a primitive model. The long-range hydrodynamic and Coulomb interactions are both taken into consideration through the Ewald summations for the first time. The major finding of our simulations is that the dependence of the long-time chain diffusivity on the Coulomb interaction strength is very different from that of the Kirkwood short-time diffusivity, which simply shows a trend nearly opposite to the chain size. When ignoring the hydrodynamic interaction (HI), the coupling effect between the chain and its counterions gives rise to a noticeable increase in the long-time diffusivity at intermediate electrostatic interaction strengths. However, the incorporation of HI suppresses this effect to a degree that one can no longer discern it. Moreover, the rotational relaxation is found to show a dependence opposite to that of the gyration radius relaxation.     

Self-diffusion in two-dimensional hard ellipsoid suspensions

We studied the self-diffusion of colloidal ellipsoids in a monolayer near a flat wall by video microscopy. The image processing algorithm can track the positions and orientations of ellipsoids with subpixel resolution. The translational and rotational diffusions were measured in both the laboratory frame and the body frame along the long and short axes. The long-time and short-time diffusion coefficients of translational and rotational motions were measured as functions of the particle concentration. We observed the nondiffusive crossover region in the intermediate time regime due to the caging of neighboring particles. Both the beginning and the ending times of the intermediate regime exhibit power-law dependence on concentration. The long-time and short-time diffusion anisotropies change nonmonotonically with concentration and reach minima in the semidilute regime because the motions along long axes are caged at lower concentrations than the motions along short axes. The time derivatives of mean-square displacements change linearly with the inverse of time in the intermediate time regimes at various particle densities. This indicates that their relaxation functions decay as 1/t which provides new challenges in theory. The effects of coupling between rotational and translational Brownian motions were demonstrated and the two time scales corresponding to anisotropic particle shape and anisotropic neighboring environment were measured.     

Dielectric studies of water clusters in cyclodextrins: Relevance to the transition between slow and fast forms of thrombin

Cyclodextrins are useful models in the study of hydrogen bonded water clusters. In alpha-cyclodextrin hexahydrate (alpha-CD.6H2O), water molecules are ordered and occupy well-defined positions whereas in the larger beta-cyclodextrin dodecahydrate (beta-CD.12H2O), there is considerable disorder with water molecules freely arranged over several possible sites. Here it is shown that beta-CD exhibits substantial structural flexibility and proton mobility compared with alpha-CD which is relatively very rigid and exhibits negligible short-range protonic conduction. These properties are directly controlled by the effective dielectric constant of the molecule, which is determined by the rotational freedom of water molecules in the hydrogen bond network. This model may be relevant to proteins where water clusters of this kind are found on the protein surface and occasionally in the protein interior. The case of thrombin, an allosteric enzyme incorporating a network of 20 internal hydrogen bonded water molecules, is discussed.     

Theoretical design of an aromatic hydrocarbon rotor driven by a circularly polarized electric field

An aromatic hydrocarbon rotor without functional groups is theoretically designed. Such a molecular rotor is free from long-range electrostatic interactions. Induced dipole interactions are the rotor-driving forces under a nonresonant excitation condition. As an example, a molecular rotor with a condensed aromatic ring, a pentacene moiety mounted on a phenyl-acetylene axle that is driven by a circularly polarized electric field is considered. Results of simulations of the quantum dynamics of a rotor that take into account short-range rotor-bath interactions are presented by numerically solving the density matrix equations of the rotational motions.     

Communication: exploring the reorientation of benzene in an ionic liquid via molecular dynamics: effect of temperature and solvent effective charge on the slow dynamics

The rotational time correlation function (RTCF) of solute benzene molecules in the ionic liquid (1-butyl-3-methylimidazolium chloride) has been studied using classical molecular dynamics simulation. The effect of solvent charge on the functional form of RTCF was investigated by comparing four force fields for the solvent where the total charge on the anion and the cation was set to ±1e, ±0.7e, ±0.5e, and 0, respectively. For all three charged solvent models, the RTCF exhibits a long-time tail where the relaxation rate exhibits a significant slowdown. This feature is strengthened by higher solvent charges as well as lower temperatures, indicating the influence of the strong Coulombic fields arising from the solvent charges. The long-time tail is caused by the extraordinarily slow solvent structural relaxation of ionic liquids compared to the time scale of their local vibrational and librational dynamics.     

Mediation of long-range attraction selectively between negatively charged colloids on surfaces by solvation

We propose a mean-field analytical model to account for the observed asymmetry in the ability to form long-range attraction by the negatively charged colloidal particles and not their equivalently charged positive counterpart. We conjecture that this asymmetry is due to solvation effects, and we phenomenologically capture its physics by considering the relative strength of this water-induced short-range repulsion between the different charge species. We then apply our model to the colloidal system of negatively charged disks that are neutralized by a sea of counterions and strongly absorbed to an interface in a compressible binary system. We demonstrate the resulting coexistence between a dilute isotropic ionic phase and a condensed hexagonal lattice phase as a function of density and interaction strength.     

Complete graph conjecture for inner-core electrons: homogeneous index case

The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model.     

Observation of a free rotation transient in hot stilbene vapor

The fluorescence anisotropy decay of collision-free trans-stilbene vapor at 463 K has been measured with 5 ps time resolution using fluorescence up-conversion. The anisotropy measured with 302 nm excitation shows a pulsewidth-limited decay attributed to free rotation followed by a constant value at longer times. The long-time anisotropy of 0.069 is close to the theoretical regular rotor value of 0.074, indicating minimal vibration-rotation energy transfer on a time scale of ≈ 50 ps. Comparison with the longtime anisotropies previously observed using shorter excitation wavelengths indicates that the rotational motion becomes more nearly statistical with increasing excess vibrational energy.     

Path integral Monte Carlo approach for weakly bound van der Waals complexes with rotations: algorithm and benchmark calculations

A path integral Monte Carlo technique suitable for the treatment of doped helium clusters with inclusion of the rotational degrees of freedom of the dopant is introduced. The extrapolation of the results to the limit of infinite Trotter number is discussed in detail. Benchmark calculations for small weakly bound (4)He(N)--OCS clusters are presented. The Monte Carlo results are compared with those of basis set calculations for the He--OCS dimer. A technique to analyze the orientational imaginary time correlation function is suggested. It allows one to obtain information regarding the effective rotational constant for a doped helium cluster based on a model for the rotational Hamiltonian. The renormalization of the effective rotational constant for (4)He(N)--OCS clusters derived from the orientational imaginary time correlation function is in good agreement with experimental results.     

Observation of a free rotation transient in hot stilbene vapor

The fluorescence anisotropy decay of collision-free trans-stilbene vapor at 463 K has been measured with 5 ps time resolution using fluorescence up-conversion. The anisotropy measured with 302 nm excitation shows a pulsewidth-limited decay attributed to free rotation followed by a constant value at longer times. The long-time anisotropy of 0.069 is close to the theoretical regular rotor value of 0.074, indicating minimal vibration-rotation energy transfer on a time scale of ≈ 50 ps. Comparison with the longtime anisotropies previously observed using shorter excitation wavelengths indicates that the rotational motion becomes more nearly statistical with increasing excess vibrational energy.     

Rotational dynamics of benzene and water in an ionic liquid explored via molecular dynamics simulations and NMR T1 measurements

The rotational dynamics of benzene and water in the ionic liquid (IL) 1-butyl-3-methylimidazolium chloride are studied using molecular dynamics (MD) simulation and NMR T(1) measurements. MD trajectories based on an effective potential are used to calculate the (2)H NMR relaxation time, T(1) via Fourier transform of the relevant rotational time correlation function, C(2R)(t). To compensate for the lack of polarization in the standard fixed-charge modeling of the IL, an effective ionic charge, which is smaller than the elementary charge is employed. The simulation results are in closest agreement with NMR experiments with respect to the temperature and Larmor frequency dependencies of T(1) when an effective charge of ±0.5e is used for the anion and the cation, respectively. The computed C(2R)(t) of both solutes shows a bi-modal nature, comprised of an initial non-diffusive ps relaxation plus a long-time ns tail extending to the diffusive regime. Due to the latter component, the solute dynamics is not under the motional narrowing condition with respect to the prevalent Larmor frequency. It is shown that the diffusive tail of the C(2R)(t) is most important to understand frequency and temperature dependencies of T(1) in ILs. On the other hand, the effect of the initial ps relaxation is an increase of T(1) by a constant factor. This is equivalent to an "effective" reduction of the quadrupolar coupling constant (QCC). Thus, in the NMR T(1) analysis, the rotational time correlation function can be modeled analytically in the form of aexp (-t/τ) (Lipari-Szabo model), where the constant a, the Lipari-Szabo factor, contains the integrated contribution of the short-time relaxation and τ represents the relaxation time of the exponential (diffusive) tail. The Debye model is a special case of the Lipari-Szabo model with a = 1, and turns out to be inappropriate to represent benzene and water dynamics in ILs since a is as small as 0.1. The use of the Debye model would result in an underestimation of the QCC by a factor of 2-3 as a compensation for the neglect of the Lipari-Szabo factor.