The fluctuating-force formulation of friction drag coefficients

A very simple and exact derivation of the relation between the fluctuating force on a brownian particle and its friction drag coefficient is presented. The fluctuating force in the present treatment is that experienced by a fixed brownian particle, rather than that experienced by a brownian particle moving along its natural trajectory in the fluid. This same treatment is extended to rotational diffusion.     

Biased diffusion in tubes formed by spherical compartments

We study the effect of the driving force on brownian motion of a point particle in a tube formed by identical spherical compartments, which create periodic entropy potential for the motion along the tube axis. The focus is on (i) the effective mobility and diffusion coefficient of the particle as functions of the driving force, (ii) localization of the particle in the central part of the tube induced by the driving force, and (iii) transit time of the particle between the openings connecting neighboring compartments. Some of the results at very small and large driving force are obtained analytically, while the majority of the results are obtained from brownian dynamics simulations.     

Fluorescence anisotropy of chromophores rotating between two reflecting barriers

A general expression is calculated for the time course of the fluorescence anisotropy of chromophores rotating about a fixed axis, with an amplitude of rotation limited by two reflecting barriers. The influence of the amplitude of these rotations on the asymptotic value of the anisotropy is discussed.     

Reaction path analysis of the "tunable" photoisomerization selectivity of free and locked retinal chromophores

Multiconfigurational second-order perturbation theory computations and reaction path mapping for the retinal protonated Schiff base models all-trans-nona-2,4,6,8-tetraeniminium and 2-cis-nona-2,4,6,8-tetraeniminium cation demonstrate that, in isolated conditions, retinal chromophores exhibit at least three competing excited-state double bond isomerization paths. These paths are associated with the photoisomerization of the double bonds in positions 9, 11, and 13, respectively, and are controlled by barriers that favor the position 11. The computations provide a basis for the understanding of the observed excited-state lifetime in both naturally occurring and synthetic chromophores in solution and, tentatively, in the protein environment. In particular, we provide a rationalization of the excited-state lifetimes observed for a group of locked retinal chromophores which suggests that photoisomerization in bacteriorhodopsin is the result of simultaneous specific "catalysis" (all-trans --> 13-cis path) accompanied by specific "inhibition" (all-trans --> 11-cis path). The nature of the S(1) --> S(0) decay channel associated with the three paths has also been investigated at the CASSCF level of theory. It is shown that the energy surfaces in the vicinity of the conical intersection for the photoisomerization about the central double bond of retinal (position 11) and the two corresponding lateral double bonds (positions 9 and 13) are structurally different.     

In situ poling and orientation stability of chromophore-bearing ladderlike polysiloxanes

A new, specially designed nonlinear optical (NLO) polymer is composed of ladderlike polysilsesquioxane as a backbone and “side-on or end-on” fixed stilbene chromophores. In-situ poling was carried out simultaneously during film formation via solvent evaporation and crosslinking which was caused by sequential hydrolysis and condensation of remained Si-H groups on macromolecules. The dipolar orientation after poling is described by an order parameter Φ which was measured using an original linear optical technique–UV dichroism. Orientation order and its decay are influenced by chromophore loading, crosslinking degree and poling condition. Compared with corresponding single chain polymers, a poled thin film of ladderlike NLO polymers demonstrates more stable poling-induced orientation.     

Brownian dynamics studies of dilute dispersions

The method of brownian dynamics of used to study the non-equilibrium properties of very dilute colloids electrostatically stabilised in dilute aqueous electrolyte. It is assumed that the colloid is a monodisperse system of structureless spherical particles embedded in a hydrodynamic continuum. Although the particles are interacting electrostatically through a screened Coulomb potential, the dilution is such that effects arising from coupling of hydrodynamic flow can be ignore. Studies of the self-diffusion coefficient and van Howe functions show that after an initial period, during which the particles move essentially independently, the flow properties of the colloids are significantly different from those expected on the basis of free brownian motion.     

Self-assembly of a hydrophobically modified naphthalene-labeled poly(acrylic acid) polyelectrolyte in water: organic solvent mixtures followed by steady-state and time-resolved fluorescence

The solution properties of two water-soluble polymers, poly(acrylic acid) (PAA), covalently labeled with the fluorescent hydrophobic dye naphthalene (Np), have been investigated in water:organic solvent mixtures. The naphthalene chromophores have been randomly attached, onto the polymer, with two different degrees of labeling. Fluorescence measurements (steady-state and time-resolved) have been used to follow the photophysical behavior of the polymers and consequently report on the self-association of the polymers in the mixed organic (methanol or dioxane):aqueous solutions. The emission spectra of the high-labeled Np PAA reveal the presence of monomer and excimer bands whereas with the low-labeled polymer only monomer emission is observed. The excitation spectra collected at the monomer and excimer emission bands show significant differences, depending on the water content of the mixture, which indicate the simultaneous presence of preformed and dynamic dimers as routes to excimer formation. The time-resolved data decay profiles of the high-labeled polymer in the mixtures were always triple exponential whereas in pure methanol and dioxane they follow biexponential laws. The data in the mixtures are consistent with two types of monomers and one excimer. Both monomers are able to give rise to excimer in the excited state, one type involving the movement of long distant Np chromophores and the other involving a local reorientation of adjacent Np chromophores. These correspond to different decay times: (1) a long which corresponds to the long distant approach of non-neighboring Np chromophores forming an excimer and (2) a short corresponding to the fast adjustment of two neighboring Np chromophores in order to have the adequate parallel geometry. An additional decay time corresponding to the excimer decay was found to be present at all wavelengths. All the decay times were dependent on the water content of the mixture. An estimation of the two excimer forming rate constants values is made for the mixed media considered in this work. On the whole, using both steady-state and time-resolved fluorescence parameters, and by comparing data for a polymer with a small number of hydrophobes with a more highly modified one, it is possible in great detail to demonstrate how association is controlled by solvent quality for the hydrophobes and by the distance between hydrophobes.     

Intramolecular energy hopping and energy trapping in polyphenylene dendrimers with multiple peryleneimide donor chromophores and a terryleneimide acceptor trap chromophore

Intramolecular F?rster-type excitation energy transfer (FRET) processes in a series of first-generation polyphenylene dendrimers substituted with spatially well-separated peryleneimide chromophores and a terryleneimide energy-trapping chromophore at the rim were investigated by steady-state and time-resolved fluorescence spectroscopy. Energy-hopping processes among the peryleneimide chromophores are revealed by anisotropy decay times of 50--80 ps consistent with a FRET rate constant of k(hopp) = 4.6 ns(-1). If a terryleneimide chromophore is present at the rim of the dendrimer together with three peryleneimide chromophores, more than 95% of the energy harvested by the peryleneimide chromophores is transferred and trapped in the terryleneimide. The two decay times (tau(1) = 52 ps and tau(2) = 175 ps) found for the peryleneimide emission band are recovered as rise times at the terryleneimide emission band proving that the energy trapping of peryleneimide excitation energy by the terryleneimide acceptor occurs via two different, efficient pathways. Molecular- modeling-based structures tentatively indicate that the rotation of the terryleneimide acceptor group can lead to a much smaller distance to a single donor chromophore, which could explain the occurrence of two energy-trapping rate constants. All energy-transfer processes are quantitatively describable with F?rster energy transfer theory, and the influence of the dipole orientation factor in the F?rster equation is discussed.     

Rotational brownian motion and fluorescence intensify fluctuations

A theory, which connects rotational brownian motion with intensity fluctuations of the light emitted from fluorescent molecules excited by linearly polarized light, is given. Analysis of rotational diffusion in this way does not depend on the close relationship between fluorescence lifetime and rotational relaxation times, which is necessary in present methods and thus makes an enlarged time range available for fluorescence spectroscopy.When short fluorescence lifetimes are used the rotational diffusion of the molecule in its ground state will be observed.     

Inertial and bias effects in the rotational brownian motion of rodlike molecules in a uniaxial potential

Inertial effects in the rotational brownian motion in space of a rigid dipolar rotator (needle) in a uniaxial potential biased by an external field giving rise to asymmetry are treated via the infinite hierarchy of differential-recurrence relations for the statistical moments (orientational correlation functions) obtained by averaging the Euler-Langevin equation over its realizations in phase space. The solutions of this infinite hierarchy for the dipole correlation function and its characteristic times are obtained using matrix continued fractions showing that the model simultaneously predicts both slow overbarrier (or interwell) relaxation at low frequencies accompanied by intermediate frequency Debye relaxation due to fast near-degenerate motion in the wells of the potential (intrawell relaxation) as well as the high frequency resonance (Poley) absorption due to librations of the dipole moments. It is further shown that the escape rate of a brownian particle from a potential well as extended to the Kramers turnover problem via the depopulation factor yields a close approximation to the longest (overbarrier) relaxation time of the system. For zero and small values of the bias field parameter h, both the dipole moment correlation time and the longest relaxation time have Arrhenius behavior (exponential increase with increasing barrier height). While at values of h in excess of a critical value however far less than that required to achieve nucleation, the Arrhenius behavior of the correlation time disappears.     

Controlling conformations in alternating dialkylsilylene-spaced donor-acceptor copolymers by a cooperative Thorpe-Ingold effect and polymer folding

A series of dialkylsilylene-spaced copolymers 6 and 7, which contain Me(2)Si and iPr(2)Si spacer groups, respectively, and have alternating donor and acceptor chromophores, have been designed and regioselectively synthesized by hydrosilylation. The ratio of the donor and acceptor chromophores for each repeat unit is 2:1, and the two donor chromophores are linked by a trimethylene bridge. A 4-aminostyrene moiety is used as the donor and a series of acceptor chromophores with different reduction potentials are employed. Both steady-state and kinetic measurements reveal that the photoinduced electron transfer (PET) in 6 obeyed the Marcus theory in which normal and inverted regions are observed. On the other hand, the iPr(2)Si-spaced copolymers 7 exhibit absorption and emission from the charge-transfer complexes exclusively due to ground-state interactions between the donor and acceptor chromophores. The discrepancy in photophysical behavior may have arisen from the difference in distance between the adjacent donor and acceptor chromophores. The bulkiness of the substituents on the silicon atom (i.e., Me versus iPr) may exert the Thorpe-Ingold effect on the local conformation around the silicon atom. The differences in the small energetic barriers for each of the conformational states may be amplified by extending the distance of the folding structure, which results in perturbing the conformation of the polymers. These results suggest that the electronic interactions between adjacent donor-acceptor pairs in these copolymers are controlled by the synchronization of the substitution effect and corresponding polymeric structures.     

Activation volumes associated with chromophore reorientation in corona poled guest–host and side-chain polymers

The decay of the second-order optical susceptibility χ⁽²⁾ as a function of temperature and pressure has been studied in a variety of corona poled guest–host and side-chain polymeric materials using second harmonic generation (SHG). The specific systems studied include the side-chain copolymer poly(disperse red 1 methacrylate-co-methyl methacrylate) (DR1-MMA) as well as the series of guest–host materials formed by individually dissolving the dyes Disperse Red 1 (DR1), Disperse Orange 3 (DO3), and N,N dimethyl-p-nitroaniline (DpNA) in poly(methyl methacrylate) (PMMA), polycarbonate (PC), and polystyrene (PS). In each of these systems, the observed relaxation of χ⁽²⁾ can be represented by a Kohlrausch-Williams-Watts stretched exponential, from which the decay time τ and decay distribution width β are determined. For pressures up to approximately 1000 atm, the natural log of the pressure shift factor is seen to vary linearly with applied pressure, yielding the activation volume for rotational reorientation of the chromophores in each system. The activation volumes are loosely correlated with dopant size in a given polymer host, but are not the same for a given dopant in different hosts. Modeling the chromophores as rotating cylinders, we show that the measured activation volumes do not correspond to the average volume swept out by the dye molecules as they reorient. On the other hand, the activation volumes for each of the three dyes dissolved in PS are seen to be in agreement with the measured activation volumes for the molecular motions associated with volume recovery in neat PS. Moreover, the activation volumes for DR1 and DpNA dissolved in PS are seen to correlate with the proposed couplings between the rotational reorientation of DR1 and the α-relaxation dynamics of PS and the slight decoupling of DpNA from the α-transition motion of PS. This correlation suggests a possible relationship between the activation volumes for chromophore reorientation and the size of the components of the host polymer or the volume swept through by the polymer components during structural reconfiguration. We demonstrate that assuming activation volumes for chromophore reorientation to be related to the size or motion of the polymer host constituents yields a consistent interpretation of the observed trends in the measured activation volumes. © 1995 John Wiley & Sons, Inc.     

Dye-containing S*c side-on/end-on copolymers

Mesomorphic copolysiloxanes, which combine 'normal' end-on linked chiral mesogenic units inducing S*_c phases and side-on fixed chromophores were prepared. The interplay of the different orientational tendencies of these moieties, which are perpendicular (end-on linked mesogenic groups) or parallel (side-on fixed chromophores) to the polymer chain, lead to a strong destabilization of the S*_c phase. However, copolymers with up to about 10 mol % of chromophores still show a smectic C* phase. FTIR measurements show that both moieties orient parallel to each other and perpendicular to the polymer chains. These copolymers are interesting to consider as coloured guest-host S*_c materials for coloured displays or as pyro-electric detectors.     

Solvation dynamics in reverse micelles: the role of headgroup-solute interactions

We present molecular dynamics simulation results for solvation dynamics in the water pool of anionic-surfactant reverse micelles (RMs) of varying water content, w(0). The model RMs are designed to represent water/aerosol-OT/oil systems, where aerosol-OT is the common name for sodium bis(2-ethylhexyl)sulfosuccinate. To determine the effects of chromophore-headgroup interactions on solvation dynamics, we compare the results for charge localization in model ionic diatomic chromophores that differ only in charge sign. Electronic excitation in both cases is modeled as charge localization on one of the solute sites. We find dramatic differences in the solvation responses for anionic and cationic chromophores. Solvation dynamics for the cationic chromophore are considerably slower and more strongly w(0)-dependent than those for the anionic chromophore. Further analysis indicates that the difference in the responses can be ascribed in part to the different initial locations of the two chromophores relative to the surfactant interface. In addition, slow motion of the cationic chromophore relative to the interface is the main contributor to the longer-time decay of the solvation response to charge localization in this case.     

Theory of diffusion-controlled reaction between non-simple molecules. II

A simplified version of the closure approximation, presented in the preceding paper, is applied to the reaction of rigid or flexible macromolecular systems. Two effects are found to be important for understanding the characteristic features of the reaction rates of these systems: (i) the orientation effect, which expresses the accessibility of the active sites, and (ii) the relaxation effect, which reflects the nature of the brownian motion of the active sites.     

Spectroscopic structure-property relationships of a series of polyaromatic platinum acetylides

To develop a structure-spectroscopic property relationship in platinum acetylides having poly(aromatic hydrocarbon) ligands, we synthesized a series of chromophores with systematic variation in the number of fused aromatic rings (nFAR) and ligand topology (polyacene (L), polyphenanthrene (Z), or compact(C)). We measured ground-state absorption, fluorescence, and phosphorescence spectra. We also performed nanosecond and femtosecond transient absorption experiments. To extend the range of compounds in the structure-property relationship, we did DFT calculations on an expanded series of chromophores. Both the DFT results and experiments show that the S(1) and T(1) state energies are a function of both nFAR and the ligand topology. In the L chromophores, the S(1) and T(1) state energies decrease linearly with nFAR. In contrast, the S(1) and T(1) state energies of the Z chromophores oscillate around a fixed value with increasing nFAR. The C chromophores have behavior intermediate between the L and Z chromophores. A parallel series of calculations on the ligands shows the same behavior. The S(1)-S(n) energy obtained from ultrafast time-resolved spectra has a linear variation in nFAR. The rate constant for nonradiative decay, k(nr), was calculated from the S(1) state lifetime and decreases with an increasing number of π electrons in the aromatic ring. The result is consistent with the spin-orbit coupling caused by the central platinum heavy atom decreasing with larger nFAR. The present work shows that the framework developed for the analysis of poly(aromatic hydrocarbon) properties is useful for the understanding of the corresponding platinum acetylide complexes.     

Conformational reorganization and solvation dynamics of dendritic oligothiophenes

We report experiments on dendritic molecules with integrated conjugated chromophores that provide microscopic mechanistic information about their solvation dynamics. The fluorescence of a series of immobilized dendritically organized oligothiophenes is studied as they are exposed to good solvents. Initially, the pi-stacking of the oligothiophene units in the dendrimer is destabilized, but full separation of the oligothiophene dendrons takes a time that is orders of magnitude longer due to barriers to torsional motion of the ester linkages. The metastable state prior to separation of the conjugated segments exhibits solution-like spectroscopy but low fluorescence quantum yield relative to the fully solvated segments. This species may play an important role in the photophysics of conjugated oligomer and polymer films. Unusual non-exponential kinetics for the oligothiophene separation step are observed and can be understood in terms of energy transfer among the dendrons.     

Brownian motion model for collision phenomena: Translational energy distribution

A brownian motion model is assumed for the relative translational motion of colliding molecules with complex internal structures and the distribution function (probability) of the final relative velocity is obtained from a Fokker-Planck equation for conditional probability in this paper. Under certain further assumptions we are able to obtain a distribution function similar in form to the information theoretic result. A formula for angular distributions is also obtained, which shows a forward-backward or a slide-way peaking, depending on the ratio of “transversal and longitudinal temperatures” (friction tensors). The “friction tensors” are given in terms of interaction potentials and can be in principle calculated from their explicit formulas given in the paper.