Addressing the challenges of modeling the scattering from bottlebrush polymers in solution

Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.     

Near-threshold electron attachment as Regge resonances: cross sections for K, Rb, and Cs atoms

We investigate the near-threshold formation of negative ions as Regge resonances in electron-atom scattering, with specific results obtained for e--K, e--Rb, and e--Cs. The complex angular momentum method, implemented within the Mulholland formulation of the total elastic cross sections, is employed. We demonstrate that for e--K, e--Rb, and e--Cs scattering, the near-threshold electron attachment cross sections are characterized by the Wigner threshold behavior, Ramsauer-Townsend minima, and Regge resonances, all discernible only through Regge partial cross section scrutiny. Regge partial, differential, and total elastic cross sections are presented and contrasted, as well as the differential cross section critical minima.     

Internally amplified stimulated Raman spectroscopy

Internally amplified stimulated Raman scattering is developed as a novel approach to study concentrational thresholds in stimulated Raman scattering (SRS). In the proposed physical model, amplifier molecules are used to bridge the spatial gaps among analyte molecules distributed distantly from each other throughout a dilute solution. As a result, Stokes photons can more effectively reach the next target molecules down the pump light path to sustain and amplify the desirable SRS process. The model has been verified by experimental results which give a better understanding of the threshold phenomenon in SRS. The technique of internal amplification is practically useful to lower concentrational thresholds, leading to improved detection limits in analytical SRS measurements.     

Equilibrium thermodynamics from basin-sampling

We present a "basin-sampling" approach for calculation of the potential energy density of states for classical statistical models. It combines a Wang-Landau-type uniform sampling of local minima and a novel approach for approximating the relative contributions from local minima in terms of the volumes of basins of attraction. We have employed basin-sampling to study phase changes in atomic clusters modeled by the Lennard-Jones potential and for ionic clusters. The approach proves to be efficient for systems involving broken ergodicity and has allowed us to calculate converged heat capacity curves for systems that could previously only be treated using the harmonic superposition approximation. Benchmarks are also provided by comparison with parallel tempering and Wang-Landau simulations, where these proved feasible.     

Photophysical hole burning in the resonance Raman excitation profile of the chlorophyll a dimer in solution

The Raman excitation profiles of normal modes of chlorophyll a dimers in hexane exhibit sharp minima between 427 and 450 nm. In this spectral range, a non-linear relationship between the Raman intensifies and the intensity of the pulsed laser is observed. These non-linearities indicate population of lower-lying excited states of the chlorophyll a dimer. The Raman scaterring from these excited states is weaker than the rigorous resonance-enhanced Raman scattering from the ground states, which leads to the observed minima.     

Are most of the stationary points in a molecular association minima? Application of Fraga's potential to benzene–benzene

The importance of characterizing the stationary points of the intermolecular potential by means of Hessian eigenvalues is illustrated for the calculation of the benzene–benzene interaction using an atom-to-atom pair potential proposed by Fraga (FAAP). Two models, the standard one-center-per atom and another using three-centers-per atom due to Hunter and Sanders, are used to evaluate the electrostatic contributions and the results are compared. It is found in both cases that although using low-gradient thresholds allows optimization procedures to avoid many stationary points that are not true minima computing time considerations makes the usual procedure of using high-gradient thresholds [say, 10^?2 kj/(mol Å)] as the most efficient. Moreover, this later procedure can be recommended because the actual minima can be characterized by means of Hessian eigenvalues even if these high-gradient thresholds are used, and further decreasing of the convergence criterion does not imply significant modifications in the geometric parameters of the minima. The possible advantages of using the three-centers-per-atom model for the calculation of molecular associations between delocalized systems are also discussed on the basis of the agreement of the benzene–benzene results with experimental and theoretical data taken from the literature. © 1993 John Wiley & Sons, Inc.     

Spatially heterogeneous dynamics and the Adam-Gibbs relation in the Dzugutov liquid

We perform molecular dynamics simulations of a one-component glass-forming liquid and use the inherent structure formalism to test the predictions of the Adam-Gibbs (AG) theory and to explore the possible connection between these predictions and spatially heterogeneous dynamics. We calculate the temperature dependence of the average potential energy of the equilibrium liquid and show that it obeys the Rosenfeld-Tarazona T(3/5) law for low temperature T, while the average inherent structure energy is found to be inversely proportional to temperature at low T, consistent with a Gaussian distribution of potential energy minima. We investigate the shape of the basins around the local minima in configuration space via the average basin vibrational frequency and show that the basins become slightly broader upon cooling. We evaluate the configurational entropy S(conf), a measure of the multiplicity of potential energy minima sampled by the system, and test the validity of the AG relation between S(conf) and the bulk dynamics. We quantify the dynamically heterogeneous motion by analyzing the motion of particles that are mobile on short and intermediate time scales relative to the characteristic bulk relaxation time. These mobile particles move in one-dimensional "strings", and these strings form clusters with a well-defined average cluster size. The AG approach predicts that the minimum size of cooperatively rearranging regions (CRR) of molecules is inversely proportional to S(conf), and recently (Phys. Rev. Lett. 2003, 90, 085506) it has been shown that the mobile-particle clusters are consistent with the CRR envisaged by Adam and Gibbs. We test the possibility that the mobile-particle strings, rather than clusters, may describe the CRR of the Adam-Gibbs approach. We find that the strings also follow a nearly inverse relation with S(conf). We further show that the logarithm of the time when the strings and clusters are maximum, which occurs in the late-beta-relaxation regime of the intermediate scattering function, follows a linear relationship with 1/TS(conf), in agreement with the AG prediction for the relationship between the configurational entropy and the characteristic time for the liquid to undergo a transition to a new configuration. Since strings are the basic elements of the clusters, we propose that strings are a more appropriate measure of the minimum size of a CRR that leads to configurational transitions. That the cluster size also has an inverse relationship with S(conf) may be a consequence of the fact that the clusters are composed of strings.     

Fitting continuum wavefunctions with complex Gaussians: Computation of ionization cross sections

We implement a full nonlinear optimization method to fit continuum states with complex Gaussians. The application to a set of regular scattering Coulomb functions allows us to validate the numerical feasibility, to explore the range of convergence of the approach, and to demonstrate the relative superiority of complex over real Gaussian expansions. We then consider the photoionization of atomic hydrogen, and ionization by electron impact in the first Born approximation, for which the closed form cross sections serve as a solid benchmark. Using the proposed complex Gaussian representation of the continuum combined with a real Gaussian expansion for the initial bound state, all necessary matrix elements within a partial wave approach become analytical. The successful numerical comparison illustrates that the proposed all-Gaussian approach works efficiently for ionization processes of one-center targets.     

Protein boson peak originated from hydration-related multiple minima energy landscape

The boson peak is a broad peak found in the low-frequency region of inelastic neutron and Raman scattering spectra in many glassy materials, including biopolymers below approximately 200 K. Here, we give a novel insight into the origins of the protein boson peak, which may also be valid for materials other than proteins. Molecular simulation reveals that the structured water molecules around a protein molecule increase the number of local minima in the protein energy landscape, which plays a key role in the origin of the boson peak. The peak appears when the protein dynamics are trapped within a local energy minimum at cryogenic temperatures. This trapping causes very low frequency collective motions to shift to higher frequencies. We demonstrate that the characteristic frequency of such systems shifts higher as the temperature decreases also in model one-dimensional energy surfaces with multiple minima.     

The influence of crystallinity distribution on small-angle x-ray scattering from semicrystalline polymers

Theoretical x-ray scattering curves have been developed for the lamellar structure in semicrystalline polymers in which there are present distributions of lamellar thickness and crystallinity. The models have been tested against samples of linear low-density, low-density and crosslinked polyethylenes. When variation in crystallinity is present in a material, a major effect is an increase in the magnitude of near-zero angle scattering. The Bragg maximum can appear as an ill-defined hump on an apparently high level of background scattering. The shape of the Bragg peak is influenced more by crystallinity distribution than by lamellar thickness distribution. Of the polymers we have studied so far only linear low density polyethylene shows significant crystallinity distribution effects. A “rule-of-thumb” method for rapid estimation of crystallinity distribution effects has been developed, obviating the need for lengthy simulation.     

A study of measured neutron elastic differential neutron cross sections for 23Na

Elastic neutron scattering angular distributions from ²³Na have been measured for incident neutron energies between 1.0 and 4.0 MeV at the University of Kentucky Accelerator Laboratory using neutron time-of-flight techniques for the scattered neutrons. This is an energy region in which existing data are very sparse. Measurements are compared with the predictions of the light particle-induced reaction code TALYS. The calculations reproduce forward angle scattering but have difficulty with relative minima in the differential cross section and large-angle scattering.     

Comparison of kinetic Monte Carlo and molecular dynamics simulations of diffusion in a model glass former

We present results from kinetic Monte Carlo (KMC) simulations of diffusion in a model glass former. We find that the diffusion constants obtained from KMC simulations have Arrhenius temperature dependence, while the correct behavior, obtained from molecular dynamics simulations, can be super-Arrhenius. We conclude that the discrepancy is due to undersampling of higher-lying local minima in the KMC runs. We suggest that the relevant connectivity of minima on the potential energy surface is proportional to the energy density of the local minima, which determines the "inherent structure entropy." The changing connectivity with potential energy may produce a correlation between dynamics and thermodynamics.     

Action spectra for photogravitropism of Phycomyces wild type and three behavioral mutants (L150, L152, and L154)

We have measured fluence rate-response curves and action spectra for photogravitropism in Phycomyces wild type and in three recently isolated mutants with elevated phototropic thresholds. The action spectra were determined from least-squares fits of a sigmoidal function to the fluence rate-response data for each wavelength. The action spectrum for wild type has maxima near 383, 413, 452, and 490 nm and minima near 397, 425, and 469 nm. This photogravitropism action spectrum is very similar to the Phycomyces phototropic balance action spectrum between 413 but has significantly higher effectiveness below 400 nm and above 490 nm. These differences may be caused by dichroic effects of the oriented receptor pigment and/or by multiple receptor pigments. The action spectra of the three mutants differ significantly from one another and from that of wild type. Relative to the wild type spectrum, all three mutants exhibit a suppression in effectiveness near 425 nm, which is near the transmission peak of the broadband blue filter used to isolate the mutants.     

Multicanonical basin hopping: a new global optimization method for complex systems

We introduce a new optimization algorithm that combines the basin-hopping method, which can be used to efficiently map out an energy landscape associated with minima, with the multicanonical Monte Carlo method, which encourages the system to move out of energy traps during the computation. As an example of implementing the algorithm for the global minimization of a multivariable system, we consider the Lennard-Jones systems containing 150-185 particles, and find that the new algorithm is more efficient than the original basin-hopping method.     

Obtaining the two-body density matrix in the density matrix renormalization group method

We present an approach that allows to produce the two-body density matrix during the density matrix renormalization group (DMRG) run without an additional increase in the current disk and memory requirements. The computational cost of producing the two-body density matrix is proportional to O(M3k2+M2k4). The method is based on the assumption that different elements of the two-body density matrix can be calculated during different steps of a sweep. Hence, it is desirable that the wave function at the convergence does not change during a sweep. We discuss the theoretical structure of the wave function ansatz used in DMRG, concluding that during the one-site DMRG procedure, the energy and the wave function are converging monotonically at every step of the sweep. Thus, the one-site algorithm provides an opportunity to obtain the two-body density matrix free from the N-representability problem. We explain the problem of local minima that may be encountered in the DMRG calculations. We discuss theoretically why and when the one- and two-site DMRG procedures may get stuck in a metastable solution, and we list practical solutions helping the minimization to avoid the local minima.     

Influence of correlations on the trajectories of zeroes of the matrix elements for bound–bound and bound–free transitions in electron scattering

The topology of the trajectories of the zeroes of the electron scattering matrix elements has been obtained in the Born approximation. At small-momentum transfer, K the behaviour of the trajectories depends on the positions and the number of Cooper minima. We demonstrate strong correlation effects in this K area. At the high momentum, the positions of the zeroes depend only slightly on the energy transfer to the atomic electron, and correlation effects are not important.     

Development of tip-enhanced optical spectroscopy for biological applications: a review

Tip-enhanced optical spectroscopy is an approach that holds a good deal of promise for the nanoscale characterisation of matter. Tip-enhanced Raman spectroscopy (TERS) has been demonstrated on a variety of samples: inorganic, organic and biological. Imaging using TERS has been shown for carbon nanotubes due to their high scattering efficiency. There are a number of compelling motivations to consider alternative approaches for biological samples; most importantly, the potential for heat damage of biomolecules and long acquisition times. These issues may be addressed through the development of tip-enhanced coherent anti-Stokes Raman scattering microscopy.     

Inherent structures for soft long-range interactions in two-dimensional many-particle systems

We generate inherent structures, local potential-energy minima, of the "k-space overlap potential" in two-dimensional many-particle systems using a cooling and quenching simulation technique. The ground states associated with the k-space overlap potential are stealthy (i.e., completely suppress single scattering of radiation for a range of wavelengths) and hyperuniform (i.e., infinite wavelength density fluctuations vanish). However, we show via quantitative metrics that the inherent structures exhibit a range of stealthiness and hyperuniformity depending on the fraction of degrees of freedom χ that are constrained. Inherent structures in two dimensions typically contain five-particle rings, wavy grain boundaries, and vacancy-interstitial defects. The structural and thermodynamic properties of the inherent structures are relatively insensitive to the temperature from which they are sampled, signifying that the energy landscape is relatively flat along the directions sampled, with wide shallow local minima and devoid of deep wells. Using the nudged-elastic-band algorithm, we construct paths from ground-state configurations to inherent structures and identify the transition points between them. In addition, we use point patterns generated from a random sequential addition (RSA) of hard disks, which are nearly stealthy, and examine the particle rearrangements necessary to make the configurations absolutely stealthy. We introduce a configurational proximity metric to show that only small local, but collective, particle rearrangements are needed to drive initial RSA configurations to stealthy disordered ground states. These results lead to a more complete understanding of the unusual behaviors exhibited by the family of "collective-coordinate" potentials to which the k-space overlap potential belongs.     

Structure of polydispersed colloids characterised by light scattering and electron microscopy

The dynamics of growth and aggregation of colloidal silver iodide particles was followed by the static light scattering method. The particles were treated as spheres and they were stable in size in the defined time interval. This approach enabled the use of the Zimm plots in order to determine the radii of gyration and the radii of spherical particles. Stable AgI colloids, either positively or negatively charged, showed the usual Zimm diagrams, while the diagrams were untypical when the stability of the colloids decreased. The untypical Zimm diagrams showed 'curves' with envelopes and 'curves' with minima in the unstable domain and in the domain where the most rapid nucleation occurs, respectively. Satisfactory agreement of particle sizes within the limits of accuracy, determined using static--and dynamic light scattering data and of the values obtained from the electron microscopic images was shown. Fitting the theoretical and experimental data, P(theta) functions showed that the particle shapes approach the theoretical model for spheres and thin discs. The colloid stability of polydispersed aggregates was also explained using the second virial coefficient, its negative sign implying interaction of particles in the solution, its positive value indicating formation of new particles from the supernatant solution. In addition, the colloid stability can be characterised by the mass fractal dimension. For positive stable colloids, Dm = 2.70 +/- 0.26, it can be related to the reaction controlled processes, whereas for negative stable colloids, Dm = 1.97 +/- 0.19, it was attributed to the diffusion controlled processes.