Forward−Backward Semiclassical Calculation of Spectral Line Shapes: I2 in a Rare Gas Cluster

A Semiclassical Framework for Mixed Quantum Classical Dynamics

Semiclassical (SC) approximations for quantum dynamic simulations in complex chemical systems range from rigorously accurate methods that are computationally expensive to methods that exhibit near-classical scaling with system size but are limited in their ability to describe quantum effects. In practical studies of high-dimensional reactions, neither extreme is the best choice: frequently a high-level quantum mechanical description is only required for a handful of modes, while the majority of environment modes that do not play a key role in the reactive event of interest are well served with a lower level of theory. In this feature, we introduce modified Filinov filtration as a powerful tool to construct mixed quantum-classical SC theories where different subsystems can be quantized to different extents without introducing ad hoc intersubsystem interaction terms. We demonstrate that these Filinov-based SC methods can systematically tune between quantum and classical limit SC behavior, offering a practical way forward to accurate and computationally efficient simulations of high-dimensional quantum processes.

Relation of exact Gaussian basis methods to the dephasing representation: theory and application to time-resolved electronic spectra

We recently showed that the dephasing representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that further acceleration is possible with cellularization [M. Šulc and J. Vaníček, Mol. Phys. 110, 945 (2012)]. Here, we focus on increasing the accuracy of this approximation by first implementing an exact Gaussian basis method, which benefits from the accuracy of quantum dynamics and efficiency of classical dynamics. Starting from this exact method, the DR is derived together with ten other methods for computing time-resolved spectra with intermediate accuracy and efficiency. These methods include the Gaussian DR, an exact generalization of the DR, in which trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. The newly obtained methods are tested numerically on time correlation functions and time-resolved stimulated emission spectra in the harmonic potential, pyrazine S0∕S1 model, and quartic oscillator. Numerical results confirm that both the Gaussian basis method and the Gaussian DR increase the accuracy of the DR. Surprisingly, in chaotic systems the Gaussian DR can outperform the presumably more accurate Gaussian basis method, in which the two bases are evolved separately.

PREFACTOR-FREE FORWARD-BACKWARD SEMICLASSICAL DYNAMICS

Within a differential expression of the Heisenberg operator, the forward and backward evolution can be joined together along a closed time contour. This manipulation leads to a dramatic cancellation of oscillations due to the two individual propagators in the Heisenberg operator and the resulting forward-backward propagator is more tractable to semiclassical approximations. This article gives a detailed description of the forward-backward semiclassical dynamics (FBSD) formalism. The semiclassical propagators, especially those of the initial value representations (IVRs), are briefly discussed. The derivation of the FBSD based on the Herman–Kluk propagator is reviewed. Different FBSD formulations with other semiclassical IVRs are worked out and numerical calculations show that they are also capable of describing quantum dynamics semiquantitatively and all display accuracy similar to the classical Wigner method.

FORWARD-BACKWARD SEMICLASSICAL SIMULATION OF DYNAMICAL PROCESSES IN LIQUIDS

Forward-backward semiclassical dynamics (FBSD) provides a practical methodology for including quantum mechanical effects in classical trajectory simulations of polyatomic systems. FBSD expressions for time-dependent expectation values or correlation functions take the form of phase space integrals with respect to trajectory initial conditions, weighted by the coherent state transform of a corrected density operator. Quantization through a discretized path integral representation of the Boltzmann operator ensures a proper treatment of zero point energy effects and of imaginary components in finite-temperature correlation functions, and extension to systems obeying Bose statistics is possible. Accelerated convergence is achieved via Monte Carlo or molecular dynamics sampling techniques and through the construction of improved imaginary time propagators. The accuracy of the methodology is demonstrated on several model systems, including models of Bose and Fermi particles. Applications to liquid argon, neon and para-hydrogen are presented.

Gaussian approximation for the structure function in semiclassical forward-backward initial value representations of time correlation functions

Initial value representations (IVRs) of semiclassical (SC) theory provide a general approach for adding quantum mechanical effects to classical molecular dynamics simulations of large molecular systems. Of the various versions of SC-IVR methodology for evaluating time correlation functions, the Fourier transform forward-backward (FB) approach is the simplest one that is able to describe true quantum coherence effects, so it is of considerable importance to find efficient and systematic ways for implementing it. It is shown in this paper that a Gaussian approximation for the "structure function"-the dependence of the correlation function on the (typically) momentum jump parameter-provides an efficient and accurate way for doing so. The approach is illustrated by an application to the time-dependent radial distribution function of I(2) (after photoexcitation) in a cluster of (up to 16) argon atoms.

Signatures of nonequilibrium solvation dynamics on multidimensional spectra

Multidimensional electronic and vibrational spectroscopies have established themselves over the last decade as uniquely detailed probes of intramolecular structure and dynamics. However, these spectroscopies can also provide powerful tools for probing solute-solvent interactions and the solvation dynamics that they give rise to. To this end, it should be noted that multidimensional spectra can be expressed in terms of optical response functions that differ with respect to the chromophore's quantum state during the various time intervals separating light-matter interactions. The dynamics of the photoinactive degrees of freedom during those time intervals (that is, between pulses) is dictated by potential energy surfaces that depend on the corresponding state of the chromophore. One therefore expects the system to hop between potential surfaces in a manner dictated by the optical response functions. Thus, the corresponding spectra should reflect the system's dynamics during the resulting sequence of nonequilibrium solvation processes. However, the interpretation of multidimensional spectra is often based on the assumption that they reflect the equilibrium dynamics of the photoinactive degrees of freedom on the potential surface that corresponds to the chromophore's ground state. In this Account, we present a systematic analysis of the signature of nonequilibrium solvation dynamics on multidimensional spectra and the ability of various computational methods to capture it. The analysis is performed in the context of the following three model systems: (A) a two-state chromophore with shifted harmonic potential surfaces that differ in frequency, (B) a two-state atomic chromophore in an atomic liquid, and (C) the hydrogen stretch of a moderately strong hydrogen-bonded complex in a dipolar liquid. The following computational methods are employed and compared: (1) exact quantum dynamics (model A only), (2) the semiclassical forward-backward initial value representation (FB-IVR) method (models A and B only), (3) the linearized semiclassical (LSC) method (all three models), and (4) the standard ground-state equilibrium dynamics approach (all three models). The results demonstrate how multidimensional spectra can be used to probe nonequilibrium solvation dynamics in real time and with an unprecedented level of detail. We also show that, unlike the standard method, the LSC and FB-IVR methods can accurately capture the signature of solvation dynamics on the spectra. Our results also suggest that LSC and FB-IVR yield similar results in the presence of rapid dephasing, which is typical in complex condensed-phase systems. This observation gives credence to the use of the LSC method for modeling spectra in complex systems for which an exact or even FB-IVR-based calculation is prohibitively expensive.

Complex-time velocity autocorrelation functions for Lennard-Jones fluids with quantum pair-product propagators

We use the pair-product approximation to the complex-time quantum mechanical propagator to obtain accurate quantum mechanical results for the symmetrized velocity autocorrelation function of a Lennard-Jones fluid at two points on the thermodynamic phase diagram. A variety of tests are performed to determine the accuracy of the method and understand its breakdown at longer times. We report quantitative results for the initial 0.3 ps of the dynamics, a time at which the correlation function has decayed to approximately one fifth of its initial value.

Semiclassical treatments for small-molecule dynamics in low-temperature crystals using fixed and adiabatic vibrational bases

Time-resolved coherent nonlinear optical experiments on small molecules in low-temperature host crystals are exposing valuable information on quantum mechanical dynamics in condensed media. We make use of generic features of these systems to frame two simple, comprehensive theories that will enable the efficient calculations of their ultrafast spectroscopic signals and support their interpretation in terms of the underlying chemical dynamics. Without resorting to a simple harmonic analysis, both treatments rely on the identification of normal coordinates to unambiguously partition the well-structured guest-host complex into a system and a bath. Both approaches expand the overall wave function as a sum of product states between fully anharmonic vibrational basis states for the system and approximate Gaussian wave packets for the bath degrees of freedom. The theories exploit the fact that ultrafast experiments typically drive large-amplitude motion in a few intermolecular degrees of freedom of higher frequency than the crystal phonons, while these intramolecular vibrations indirectly induce smaller-amplitude--but still perhaps coherent--motion among the lattice modes. The equations of motion for the time-dependent parameters of the bath wave packets are fairly compact in a fixed vibrational basis/Gaussian bath (FVB/GB) approach. An alternative adiabatic vibrational basis/Gaussian bath (AVB/GB) treatment leads to more complicated equations of motion involving adiabatic and nonadiabatic vector potentials. Computational demands for propagation of the parameter equations of motion appear quite manageable for tens or hundreds of atoms and scale similarly with system size in the two cases. Because of the time-scale separation between intermolecular and lattice vibrations, the AVB/GB theory may in some instances require fewer vibrational basis states than the FVB/GB approach. Either framework should enable practical first-principles calculations of nonlinear optical signals from molecules in cryogenic matrices and their semiclassical interpretation in terms of electronic and vibrational decoherence and vibrational population relaxation, all within a pure-state description of the macroscopic many-body complex.

Forward−Backward Semiclassical Dynamics with Information-Guided Noise Reduction for a Molecule in Solution

The forward--backward semiclassical dynamics (FBSD) methodology is used to obtain expressions for time correlation functions of a system (atom or molecule) in solution. We use information-guided noise reduction (IGNoR) [Makri, N. Chem. Phys. Lett. 2004, 400, 446] to minimize the statistical error associated with the Monte Carlo integration of oscillatory functions. This is possible by reformulating the correlation function in terms of an oscillatory solvent-dependent contribution whose integral can be obtained analytically and a slowly varying function obtained via a grid-based iterative evaluation of solute properties. Knowledge of the exact integral of the oscillatory function, combined with correlated statistics, leads to partial cancellation of the Monte Carlo error. Application on a one-dimensional solute-solvent model shows a substantial improvement of convergence in the IGNoR-enhanced FBSD correlation function for a fixed number of Monte Carlo samples. The reduction of statistical error achieved by using the IGNoR methodology becomes more significant as the number of solvent particles increases.

Optimized Monte Carlo sampling in forward–backward semiclassical dynamics

Forward-backward semiclassical dynamics (FBSD) provides a rigorous and powerful methodology for calculating time correlation functions in condensed phase systems characterized by substantial quantum mechanical effects associated with zero-point motion, quantum dispersion, or identical particle exchange symmetries. The efficiency of these simulations arises from the use of classical trajectories to capture all dynamical information. However, full quantization of the density operator makes these calculations rather expensive compared to fully classical molecular dynamics simulations. This article discusses the convergence properties of various correlation functions and introduces an optimal Monte Carlo sampling scheme that leads to a significant reduction of statistical error. A simple and efficient procedure for normalizing the FBSD results is also discussed. Illustrative examples on model systems are presented.

A nonperturbative calculation of nonlinear spectroscopic signals in liquid solution

Nonlinear spectroscopic signals in liquid solution were calculated without treating the field-matter interaction in a perturbative manner. The calculation is based on the assumption that the intermolecular degrees of freedom can be treated classically, while the time evolution of the electronic state is treated quantum mechanically. The calculated overall electronic polarization is then resolved into its directional components via the method of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)]. It is shown that the time dependence of the directional components is independent of laser intensity in the impulsive pulse regime, which allows for flexibility in choosing the procedure for calculating optical response functions. The utility and robustness of the nonperturbative procedure is demonstrated in the case of a two-state chromophore solvated in a monoatomic liquid, by calculating nonlinear time-domain signals in the strong-field, weak-field, impulsive, and nonimpulsive regimes.

Morphology Phase Diagram of Ultrathin Anatase TiO2Films Templated by a Single PS-b-PEO Block Copolymer

Ultrathin TiO2 films showing rich morphologies are prepared on Si(100) substrates using sol-gel chemistry coupled with an amphilic polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymer as a structure-directing agent. The block copolymer undergoes a good-poor solvent pair induced phase separation in a mixed solution of 1,4-dioxane, concentrated hydrochloric acid (HCl), and titanium tetraisopropoxide (TTIP). By adjusting the weight fractions of 1,4-dioxane, HCl, and TTIP, inorganic block copolymer composite films containing a variety of different morphologies are obtained. On the basis of the results a ternary phase diagram of the morphologies is mapped. By calcination, anatase TiO2 films are achieved. The morphologies and crystallographic phase of the films are studied with AFM, SEM, and XRD, respectively, and the formation mechanisms of the different morphologies are discussed.

Generation of polymerosomes from double-emulsions

Diblock copolymers are known to spontaneously organize into polymer vesicles. Typically, this is achieved through the techniques of film rehydration or electroformation. We present a new method for generating polymer vesicles from double emulsions. We generate precision water-in-oil-in-water double emulsions from the breakup of concentric fluid streams; the hydrophobic fluid is a volatile mixture of organic solvent that contains dissolved diblock copolymers. We collect the double emulsions and slowly evaporate the organic solvent, which ultimately directs the self-assembly of the dissolved diblock copolymers into vesicular structures. Independent control over all three fluid streams enables precision assembly of polymer vesicles and provides for highly efficient encapsulation of active ingredients within the polymerosomes. We also use double emulsions with several internal drops to form new polymerosome structures.

Dilution-Induced Spheres-to-Vesicles Morphological Transition in Micelles from Block Copolymer/Surfactant Complexes

Metastable spherical micelles have been obtained by mixing in chloroform poly(styrene)-block-poly(4-vinylpyridine) diblock copolymers with perfluorinated surfactants bearing a carboxylic acid head. Dilution of these initial micelles triggers a morphological reorganization resulting in the formation of more stable vesicles. This transition can be advantageously used to encapsulate molecules of interest.

Visualizing Worm Micelle Dynamics and Phase Transitions of a Charged Diblock Copolymer in Water

Assemblies of block copolymer amphiphiles are sometimes viewed as glassy, frozen, or static colloids, especially in strongly segregating solutions. Here, we visualize by fluorescence microscopy and AFM the dynamics and transitions of single cylindrical micelles and vesicles composed of a charged diblock copolymer in water. In mapping the salt- and pH-dependent phase diagrams of a near-symmetric diblock of poly(acrylic acid)-polybutadiene, low pH and high salt (NaCl, CaCl2) neutralize and screen the charged corona sufficiently to foster membrane formation and generate vesicles. Decreased salt and neutral pH increases intra-coronal repulsion and drives a transition to multi-branched cylinders and highly stable, but fluid and flexible, worm micelles. Ca2+ both stiffens cylinders and stabilizes them relative to spheres. Further increase of intra-coronal repulsion generates spherical micelles by fragmentation and pinch-off at the ends of worms. Both the transition kinetics and phase diagrams indicate divalent cation is about 5-10-fold more effective than monovalent in stabilizing all nonspherical morphologies.

A comparison between different semiclassical approximations for optical response functions in nonpolar liquid solutions

The temporal behavior of optical response functions (ORFs) reflects the quantum dynamics of an electronic superposition state, and as such lacks a well-defined classical limit. In this paper, we consider the importance of accounting for the quantum nature of the dynamics when calculating ORFs of different types. To this end, we calculated the ORFs associated with the linear absorption spectrum and the nonlinear two-pulse photon-echo experiment, via the following approaches: (1) the semiclassical forward-backward approach; (2) an approach based on linearizing the path-integral forward-backward action in terms of the difference between the forward and backward paths; (3) an approach based on ground state nuclear dynamics. The calculations were performed on a model that consists of a two-state chromophore solvated in a nonpolar liquid. The different methods were found to yield very similar results for the absorption spectrum and "diagonal" two-pulse photon echo (i.e., the homodyne-detected signal at time t=t(0) after the second pulse, where t(0) is the time interval between the two pulses). The different approximations yielded somewhat different results in the case of the time-integrated photon-echo signal. The reasons for the similarity between the predictions of different approximations are also discussed.

A semiclassical generalized quantum master equation for an arbitrary system-bath coupling

The Nakajima-Zwanzig generalized quantum master equation (GQME) provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a, possibly anharmonic, quantum bath. In this equation, a memory kernel superoperator accounts for the influence of the bath on the dynamics of the system. In a previous paper [Q. Shi and E. Geva, J. Chem. Phys. 119, 12045 (2003)] we proposed a new approach to calculating the memory kernel, in the case of arbitrary system-bath coupling. Within this approach, the memory kernel is obtained by solving a set of two integral equations, which requires a new type of two-time system-dependent bath correlation functions as input. In the present paper, we consider the application of the linearized semiclassical (LSC) approximation for calculating those correlation functions, and subsequently the memory kernel. The new approach is tested on a benchmark spin-boson model. Application of the LSC approximation for calculating the relatively short-lived memory kernel, followed by a numerically exact solution of the GQME, is found to provide an accurate description of the relaxation dynamics. The success of the proposed LSC-GQME methodology is contrasted with the failure of both the direct application of the LSC approximation and the weak coupling treatment to provide an accurate description of the dynamics, for the same model, except at very short times. The feasibility of the new methodology to anharmonic systems is also demonstrated in the case of a two level system coupled to a chain of Lennard-Jones atoms.

Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range

Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.

SEMICLASSICAL DESCRIPTION OF MOLECULAR DYNAMICS BASED ON INITIAL-VALUE REPRESENTATION METHODS

Recent progress in the development of semiclassical methods to describe quantum effects in molecular dynamics is reviewed. Focusing on rigorous semiclassical methods that are based on the initial-value representation of the semiclassical propagator, we discuss several promising schemes that have been developed in the past few years to extend the applicability of semiclassical approaches to complex molecular systems. In particular, integral-filtering techniques and forward-backward methods are surveyed. Furthermore, recently proposed approaches that allow the semiclassical description of nonadiabatic molecular dynamics are discussed. The potential and efficiency of these methods is illustrated by selected applications.

Polystyrene-b-poly(acrylic acid) vesicle size control using solution properties and hydrophilic block length

Polymeric vesicles have attracted considerable attention in recent years, since they are a model for biological membranes and have versatile structures with several practical applications. In this study, we prepare vesicles from polystyrene-b-poly(acrylic acid) block copolymer in dioxane/water and dioxane/THF/water mixtures. We then examine the ability of additives (such as NaCl, HCl, or NaOH), solvent composition, and hydrophilic block length to control vesicle size. Using turbidity measurements and transmission electron microscopy (TEM) we show that larger vesicles can be prepared from a given copolymer by adding NaCl or HCl, while adding NaOH yields smaller vesicles. The solvent composition (ratio of dioxane to THF, as well as the water content) can also determine the vesicle size. From a given copolymer, smaller vesicles can be prepared by increasing the THF content in the THF/dioxane solvent mixture. In a given solvent mixture, vesicle size increases with water content, but such an increase is most pronounced when dioxane is used as the solvent. In THF-rich solutions, on the other hand, vesicle size changes only slightly with the water concentration. As to the effect of the acrylic acid block length, the results show that block copolymers with shorter hydrophilic blocks assemble into larger vesicles. The effect of additives and solvent composition on vesicle size is related to their influence on chain repulsion and aggregation number, whereas the effect of acrylic acid block length occurs because of the relationship among the block length, the width of the molecular weight distribution, and the stabilization of the vesicle curvature.

Onset of decoherence: Six-wave mixing measurements of vibrational decoherence on the excited electronic state of I2 in solid argon

Pump-probe, four-wave, and six-wave mixing measurements of I2 isolated in solid argon are used to provide a clear experimental measure for the onset of vibrational quantum decoherence on the excited electronic state. The electronically resonant, six-wave mixing measurements bypass the rapid electronic dephasing, and measure the quantum cross-correlation between two packets launched on the B-state. The vibrational quantum coherence survives one period of motion, 400 fs, during which approximately 2000 cm(-1) of energy is transferred to the lattice. The decoherence occurs during the second cycle of motion, while classically coherent motion measured via pump-probe spectroscopy using the same electronic resonances continues for approximately 15 periods. This is contrasted with vibrational dephasing on the ground electronic surface, which lasts for 10(2) periods, as measured through time-resolved coherent anti-Stokes Raman scattering. The measurements and observables are discussed through time-circuit diagrams, and a mechanistic description of decoherence is derived through semiclassical analysis and simulations that reproduce the experiments.

Quantum initial value representation simulation of water trimer far infrared absorption spectrum

We extend the technique of quantum propagation on a grid of trajectory guided coupled coherent states to simulate experimental absorption spectra. The approach involves calculating the thermally averaged dipole moment autocorrelation function by means of quantum propagation in imaginary time. The method is tested on simulation of the far infrared spectrum of water trimer based on a three-dimensional model potential. Results are in good agreement with experiment and with other calculations.

Effect of poly(acrylic acid) block length distribution on polystyrene-b-poly(acrylic acid) block copolymer aggregates in solution. 2. A partial phase diagram

The first paper of the series, which focused on the effect of polydispersity on the self-assembly of block copolymer vesicles, showed that an increase in the width of the poly(acrylic acid) (PAA) block length distribution resulted in a decrease in the size of the vesicles formed. In this paper, the rest of the phase diagram is explored. For the present study, a series of polystyrene-b-poly(acrylic acid) copolymers of an identical polystyrene length of 325 units but of varying degrees of polymerization of PAA was synthesized. Mixtures of the copolymers were made to artificially broaden the molecular weight distribution of PAA at a constant number average of 48 in the polydispersity index (PDI) range of 1.1-3.3. The mixtures were dissolved in dioxane, and water was added slowly to predetermined amounts. Transmission electron microscopy was used to observe aggregate morphologies at different water contents and PAA PDIs. At low water contents, dynamic light scattering was also used to measure the sizes of the aggregates. A partial phase diagram as a function of the water content and PAA PDI was obtained. Large compound micelles and spherical micelles (average diameter of 40 nm) were found at low water contents; however, at a water content of 12% (w/w), a continuum of morphologies from spheres to rods to vesicles was found with increasing PAA PDI. In addition, each copolymer was investigated by itself under identical conditions to those used for the mixtures to determine if there was any segregation of the individual polymers into separate aggregates. No evidence for such segregation was found.

Semiclassical calculation of the vibrational echo

The infrared echo measurement probes the time scales of the molecular motions that couple to a vibrational transition. Computation of the echo observable within rigorous quantum mechanics is problematic for systems with many degrees of freedom, motivating the development of semiclassical approximations to the nonlinear optical response. We present a semiclassical approximation to the echo observable, based on the Herman-Kluk propagator. This calculation requires averaging over a quantity generated by two pairs of classical trajectories and associated stability matrices, connected by a pair of phase-space jumps. Quantum, classical, and semiclassical echo calculations are compared for a thermal ensemble of noninteracting anharmonic oscillators. The semiclassical approach uses input from classical mechanics to reproduce the significant features of a complete, quantum mechanical calculation of the nonlinear response.

Energy conserving approximations to the quantum potential: Dynamics with linearized quantum force

Solution of the Schrodinger equation within the de Broglie-Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact time-evolution of a correlated Gaussian wave function in a locally quadratic potential. The method is computationally cheap in many dimensions, conserves total energy and satisfies the criterion on the average quantum force. Expectation values are readily found by summing over trajectory weights. Efficient extraction of the phase-dependent quantities is discussed. We illustrate the efficiency and accuracy of the linear quantum force approximation by examining a one-dimensional scattering problem and by computing the wavepacket reaction probability for the hydrogen exchange reaction and the photodissociation spectrum of ICN in two dimensions.

Interfacial solubilization of model amphiphilic molecules in block copolymer micelles

We investigate the solubilization of 2-nitrodiphenylamine, a hydrophobic but polar dye molecule, in aqueous solutions of polystyrene(310)-b-poly(acrylic acid)(47) micelles. The solubilization capacity of the micelles, which consist of a polystyrene core and poly(acrylic acid) corona, and the micelle-water partition coefficient are evaluated as a function of the solubilizate concentration. The solubilization isotherm shows a nonlinear behavior, and the partition coefficient, instead of being constant, is strongly dependent on the dye concentration. These results are explained by treating solubilization as a binding process, and by fitting the data to a Langmuir adsorption model. In addition, we examine the locus of solubilization of 2-nitrodiphenylamine using its solvatochromic properties and solubility in model solvents, and we identify the micellar interface as the solubilization site. Confirmatory studies, including the dependence of solubilization on the interfacial area of the aggregates, the role of the poly(acrylic acid) corona chains in stabilizing the solubilized molecules, and the effect of the solubilizate structure on the extent of incorporation, were also conducted. The results, consistent with surface localization, show that solubilization is dependent on the interfacial area of the aggregates, and on the affinity of the solubilizate for the micellar interface.

Preparation and pH Triggered Inversion of Vesicles from Poly(acrylic Acid)-block-Polystyrene-block-Poly(4-vinyl Pyridine)

The aggregate morphologies of the biamphiphilic triblock PAA(26)-b-PS(890)-b-P4VP(40) have been studied by TEM as a function of pH in DMF/THF/H(2)O mixtures. The outside surfaces of the aggregates were characterized by zeta potential measurements. Starting at the apparent pH (pH) of 1, and increasing gradually to pH14, the aggregate morphologies of this triblock change progressively from vesicles (pH1), to solid spherical or ellipsoidal aggregates (pH3 approximately 11), and finally back to vesicles (pH14). Vesicles prepared at pH1 contain P4VP chains on the outside and PAA chains on the inside, while those prepared from the same triblock at pH14 contain PAA outside and P4VP inside. The segregation is based on the difference in repulsive interactions within the PAA or P4VP corona under different pH conditions. At low pH, the curvature is stabilized through increased repulsive interactions between the P4VP chains on the outside relative to the less repulsive interactions between the PAA chains on the inside. At pH14, by contrast, the PAA is preferentially segregated to the outside and the P4VP to the inside because of the increased repulsive interaction between PAA chains and the decreased repulsive interaction between P4VP chains at high pH. Most importantly, vesicles with PAA on the outside can be inverted to P4VP on the outside by changing the pH while the vesicles have swollen cores and are under dynamic conditions. The conversion mechanism is suggested to involve a whole vesicle process because the CMC is far too low for single chain reassembly to be involved.