Encounter Distance Research Articles

Encounter probabilities between male and female rotifers

The relationship between population density and sexual reproduction is explored for planktonic rotifer populations. It has been argued that selection favors sex at population maxima because of favorable probabilities of encounter. Factors determining the probability of encounter are examined. Experimentally determined parameters for males and females (swimming speed, duration of fertility, net fecundity, and encounter distance) are used to investigate density effects on the probability of encounter. As population density increases, the probability of encounter also increases sigmoidally. The probability of a female encountering a male during her fertile period begins to increase rapidly at ≈ 50 males/1. The increase continues until it becomes asymptotic at ≈ 1000 males/1, where the probability of a female encountering, at least one male during her fertile period approaches one. The duration of female fertility is less than that of males, causing the female curve to be displaced toward higher population densities. Critical density, the population density where R o ′ is exactly equal to one, for males and females is 11.7 and 141 individuals/1, respectively. The precision of the model was evaluated by observing the frequency of male-female encounters during 212 5-min observation periods. The observed encounter rate was 1.49/min, compared to a predicted rate of 1.53/ min. These values are not significantly different as determined by t-test. The constraints placed on the timing of sex by population density are discussed.

Chemistry of exciplexes. 19. Exciplex-promoted electron transfer in 1-(phenylamino)-3-(9-anthryl)propanes

Light-induced electron transfer in multicomponent systems and polychromophoric molecules is a subject of current interest. In nonpolar media, a photoexcited molecular may react with a ground-state molecule in a specific orientation yielding an exciplex which may be characterized by its fluorescence. Exciplexes may be deactivated by another ground-state molecule, and it has been suggested that electron transfer may play a role in this deactivation. However, this suggestion was not supported by any direct experimental evidence. A photoexcited molecule may react with a ground-state molecule to undergo electron transfer at an encounter distance yielding a radical ion pair in polar media. These radical ions tend to undergo rapid back electron transfer to revert back to substrates in their ground state or triplet state. In order to convert light energy into chemical energy in an efficient manner, the rate of back electron transfer must be controlled or retarded. In this investigation, the authors examined the reactive intermediates generated from photoexcited polychromophoric systems by kinetic spectroscopy. The compounds used were 1-3 containing an anthryl group as the photoexcited acceptor and one or two dialkylanilino groups as the donor(s). The intermediates derived from these photoexcited compounds, the anthryl radical anion, dialkylanilino radical cation, andmore » anthryl triplet all exhibit well-defined absorption characteristics. This paper demonstrates that an exciplex may undergo electron transfer with another donor molecule in dichloromethane and the lifetimes of ions generated in such a system are substantially longer than the lifetimes of ions from analogous electron transfer in polar media.« less

An improved thermal model for cometary nuclei

We have modified our earlier thermal model of cometary nuclei by incorporating a more accurate calculation of the opacity of the cometary dust coma. The new model uses a modified Sekanina‐Miller dust particle size distribution and a Delsemme‐Miller gas outflow dynamics model. The improved model has been applied to the case of the 1986 apparition of Halley's Comet, also incorporating a revised radius and albedo for the Halley nucleus. The estimated opacity of the Halley coma is reduced from that of the earlier model. The revised opacity is 0.12 at 1.0 AU and 0.43 at perihelion, 0.587 AU. This results in a decrease in the energy supplied to the nucleus from the coma by multiply scattered radiation and thermal emission, and brings the model into better agreement with the results of others. The coma feedback mechanism enhances nucleus gas production by a factor of 1.4 at 1.0 AU over that for a bare ice nucleus with no dust coma, and by a factor of 2.3 at perihelion. Predicted gas production at 0.9 AU postperihelion, the expected heliocentric encounter distance for the Giotto mission, is 4.4×1029 molecules per second. This agrees well with a recent estimate of 3.9×1029 molecules s−1 for the Halley gas production rate at 0.9 AU during the 1910 apparition.

On the fluorescence quenching of pyrene by iodine

Fluorescence quenching of the excited state of pyrene by iodine in cyclohexane and methano is studied. Quenching rate constants for deactivation of K Q = 2.20±0.02 × 10 10 mol −1 s −1 dm 3 and K Q = 1.63±0.06 × 10 10 mol −1 s −1 dm 3 are measured for pyrene in cyclohexane and methanol, respectively. These values are discussed in terms of a diffusion-controlled mechanism. Exchange quenching process in cyclohexane, giving an “effective” encounter distance of about 13.3 Å is proposed.

ChemInform Abstract: EFFECT OF PERFLUOROCARBONS ON THE ULTRAVIOLET ABSORPTION AND FLUORESCENCE CHARACTERISTICS OF SOME SATURATED HYDROCARBON LIQUIDS

Perfluoro-n-alkanes and perfluorocycloalkanes are found to affect the photophysical properties of saturated hydrocarbons in markedly different ways.The addition of a low concentration (<0.2 M) of a perfluoro-n-alkane to a hydrocarbon liquid has no observable effect on the electronic absorption spectrum and only very slightly quenches the hydrocarbon fluorescence. In contrast, at the same concentration levels, the perfluorocycloalkane strongly perturbs the absorption spectrum and very effectively reduces the fluorescence quantum yield. The change in the absorption spectrum is attributed to a contact charge-transfer absorption with the hydrocarbon acting as electron donor. The efficiency with which the perfluorocycloalkane reduces the hydrocarbon fluorescence quantum yield increases with increasing perfluorocycloalkane concentration. The results are analyzed with a conventional diffusional model that includes transient terms. The model contains two parameters, an encounter distance, R, and the product of the relative diffusion coefficient, D, and the lifetime, tau/sub 0/, of the hydrocarbon excited state. The model is applied to perfluorodecalin quenching of cyclohexane, decalin, and 2,3-dimethylbutane at excitation wavelengths, lambda/sub ex/, ranging from 185 to 147 nm. An unrestricted, two-parameter, least-squares fit of the model to the data provides values of R and D(tau/sub 0/) for each solvent system at each lambda/sub ex/. Where values ofmore » D and tau/sub 0/ are known independently, their product agrees well with the D(tau/sub 0/) obtained from the fit. The value of R is found to be approx. = 14 angstrom for all solvents at all lambda/sub ex/. This value is estimated to be about 2 times larger than the ground-state hydrocarbon-perfluorodecalin contact distance.« less

Long range quenching of triplet phenanthrene by copper ions in the liquid phase

The quenching of triplet phenanthiene by Cu 2+ has been studied over a range of high viscosities. The rate constants were determined in the time-dependent regime and are compatible with an encounter distance which increases with increasing viscosity. The Smoluchowski analysis of the time-dependence breaks down at very high viscosities in agreement with a numerical analysis.

Direct observation of excimer formation in anthracene and 9,9′-bianthryl

The existence of anthracene excimer in fluid solution was confirmed for the first time by observing the coincidence of the rise time of excimer fluorescence with the decay time of monomer fluorescence with the use of a picosecond laser, a streak camera, and a computer. The continuum model of diffusion theory is found to be applicable to the excimer formation and the encounter distance between anthracene in the excited state and that in the ground state is calculated to be 8 ± 2 Å. The anomalously broad featureless fluorescence observed for 9,9′-bianthryl in glycerol-methanol (9:1) solution was found to be emitted from the species formed only in the excited state and its rise time was found to be coincident with the decay time of fluorescence from anthracene moiety composing 9,9′-bianthryl, α,ω-9,9′-bianthrylpropane, -butane, -hexane, and -dodecane were found not to form excimer in the excited state.

Solution of the Smoluchowski equation with a Coulomb potential. II. Application to fluorescence quenching

The rate of fluorescence quenching is derived for the continuum model of a diffusion-controlled reaction, using the exact solution to the Smoluchowski equation with a Coulomb potential derived earlier. The first two terms in the long-time expansion of the reaction rate are formally the same as the result obtained by Smoluchowski for no long-range forces. However, the sum of the hard-core radii in Smoluchowski’s expression is replaced by an effective encounter distance. Our expression for the reaction rate with the Coulomb interaction constitutes an extension of Debye’s steady-state result to the transient case.

QUENCHING OF CHLOROPHYLL FLUORESCENCE BY NITROBENZENE

Abstract—Nitrobenzene quenching of chlorophyll fluorescence in ethanol has been investigated. Steady state relative quantum yields have been measured and fluorescence decay rates were determined using both nanosecond photon counting and picosecond pulses from a mode‐locked Nd3+ glass laser.The fluorescence decay is described by1(t)=I0 exp (‐t/τ−At1/2)the form predicted for decay governed by the kinetics of the continuum model of diffusion controlled reactions. From the parameters of the fluorescence decay, the encounter distance is 5–7 A° the mutual diffusion coefficient is 0.62 × 10‐‐5 cm2s‐1± 12%.Some of the fluorescence quenching is also attributed to static quenching by a nitrobenzene‐chlorophyll, ground‐state complex. The equilibrium constant for formation of this ground‐state complex was determined to be 4.1 M‐1. The combined dynamic and static quenching model allows calculation of quantum yields of fluorescence in good agreement with the experimentally determined quantum yields.

Numerical investigation of tunnelling contributions to electron scavenging reactions in liquids at short times

Fick's second diffusion equation, with an added exponential sink term, is integrated numerically to simulate the decay of electrons at short times in the presence of scavengers. The time dependence of the scavenger concentration profile, the scavenging rate constant, and the electron concentration are illustrated graphically. Using the experimental results of Buxton et al. and Jonah et al. It is shown that the Smoluchowski equation is valid within their experimental time ranges provided the cage encounter distance is replaced by Reff, where Reff can be evaluated explicitly in terms of reaction parameters. It is also shown that tunnelling from relaxed traps may make a significant contribution to ultra-short time electron scavenging.

Investigations on purine and pyrimidine bases stacking associations in aqueous solutions by the fluorescence quenching method. I. Autoassociation of 2-aminopurine.

A general equation was derived, describing fluorescence quantum yield and lifetime of an autoassociating compound in liquid solutions. The autoassociation of 2-aminopurine in aqueous solution was examined within the range from 0 to 90 degrees C. The compound seemed to associate cooperatively. The thermodynamic parameters of polymerization change with temperature, so that its free enthalypy deltaG = 0.0797 T2 + 45.4 T - 7893. The dimerization enthalpy and entropy are approximately temperature-independent (deltaH2 = -4.17 kcal/mol deltas2 = -10.9 e.u.), although the function: delta g2 = -0.0308T2 +30.3T - 7213 fits experimental points better. The observed dependences can be explained by the increasing role of the hydrophobic effect with temperature and size of the aggregates. The association rate constants were determined, and a two-step reaction mechanism was demonstrated. The first step is diffusion-controlled. The second is characterized by an activation energy of approximately 2 kcal/mol and an encounter distance of approximately 8.3 angstroms.

An investigation of the electronic and steric environments of tyrosyl residues in ribonuclease a and Erwinia Carotovoral-asparaginase through fluorescence quenching by caesium, iodide and phosphate ions

The fluorescence lifetimes and relative quantum yields of several derivatives of tyrosine are reported. The quenching of the fluorescence of these compounds by phosphate, caesium and iodide ions has been investigated; the encounter rate constants, calculated from the quenching parameters and lifetimes, show a clear dependence on the charges borne by quenchers and fluorophores. The ratio of the Stern-Volmer constants of iodide and caesium, ions of similar size, defines an electrostatic parameter sensitive to the charge of the fluorophore which can be evaluated without knowledge of the fluorescence lifetimes. The mean of the encounter rate constants for caesium and iodide ions defines a rate constant which is largely charge-independent and is used to establish a steric parameter. The two parameters are used to investigate the tyrosine environment in bovine ribonuclease A (EC 3.1.4.23) and Erwinia carotovora l-asparaginase (EC 3.5.1.1). The quantum yield of l-asparaginase (0.12) is very high for a class A protein and may be associated with the absence of disulphide bridges. There was no evidence for more than one type of tyrosine residue from the quenching experiments with either enzyme, an observation which is attributed to efficient energy transfer amongst tyrosine residues. At pH values close to the isoelectric points of the enzymes the electrostatic parameter suggests that the environment of the quenchable tyrosines in l-asparaginase is somewhat more positive than in ribonuclease. In 1% sodium dodecyl sulphate the tyrosine environment of l-asparaginase becomes markedly negative as expected. The steric parameter indicates a lower accessibility of the tyrosine residues in l-asparaginase than in ribonuclease; an illustrative calculation is provided linking the steric parameter with the number of exposed tyrosine residues by taking into account the greater collision frequency of the larger protein molecules and the encounter distance for quenching determined from charge effects on the quenching of the model compounds. The calculation suggests that three tyrosyl residues are accessible in ribonuclease, in good agreement with other studies, but in l-asparaginase the number increases from 0.4 at pH 5.73 to 0.8 at pH 9.16 suggesting a loosening of the enzyme structure at high pH.

Long range energy transfer by dipole–dipole and exchange interactions in rigid media and in liquids

Static quenching by dipole–dipole and exchange mechanisms is discussed in terms of a time dependent radial density function, which describes the distribution of acceptor molecules around donors. The final equations for the time dependence of the donor concentration agree with those derived previously using an alternative technique. The radial density function provides a helpful physical insight into the short comings of the active sphere treatment. The effect of an exchange interaction on diffusion-controlled reactions is discussed, and an analytic equation derived for the increase in the effective encounter distance as the diffusion coefficient decreases. The transition from diffusive to static quenching is discussed, and the two regions linked qualitatively.

Theoretical model for diffusion controlled reactions of solvated electrons, incorporating a tunnelling mechanism

The effect on diffusion-controlled reactions, of electron tunnelling from a solvent cavity to a scavenger molecule, is examined. The radial diffusion equation is modified to include a sink term, which varies exponentially with distance from the origin, and thus simulates tunnelling behaviour. An analytical solution is obtained for the steady-state, and applied to diffusion controlled reactions of the solvated electron in media covering a wide range of viscosities. In low viscosity media (η∼10–3 kg m–1 s–1) reaction can take place at a reactant separation of about two molecular diameters, this distance increases with viscosity, reaching about eight molecular diameters for η= 109 kg m–1 s–1. The theory is also applied to energy transfer by an exchange mechanism; transfer only begins to take place from distances greater than the encounter distance when the viscosity reaches ∼105 kg m–1 s–1.

The direct observation of transient effects in diffusion-controlled fluorescence quenching

Direct observation of the influence of so-called transient terms in the theory of diffusion-controlled reactions is reported for the fluorescence decay of a quenched system. It is found that the decay law of the quenched system accurately follows exp (- At - Br 1 2 ) as required by simple continuum theory. Values for the two adjustable parameters, R′ and D, the encounter distance and the sum of the diffusion coefficients are obtained and compared with values obtained from steady-state measurements.

Intermediates and Kinetics of Fluorescence Quenching by Electron Transfer

AbstractA structureless, longwavelength fluorescence band, attributed to the excited (charge‐transfer) complex: A−D+, occurs when the fluorescence of aromatic hydrocarbons (A) is quenched by aryl amines (D). The relative intensity of this band is found to decrease strongly with increasing solvent polarity, so that ultimately in highly polar solvents (ε &gt; 30) no complex emission can be observed even at high aryl amine concentration at which the normal hydrocarbon fluorescence is strongly quenched.Flash experiments carried out with solutions of aromatic hydrocarbons in acetonitrile (ε = 37) with high concentrations of diethylaniline show transient absorption spectra which are due to the triplet state of the hydrocarbon and to the radical ions A·− and D+ which are produced with quantum yields between 2 and 6%. Kinetic experiments (of fluorescence quenching) indicate that in polar solvents electron transfer can occur at an encounter distance of about 7 Å. A kinetic scheme which is consistent with these results and meets the energetic requirements is discussed.