Diffusion-controlled Limit Research Articles

Guest Binding Dynamics with Cucurbit[7]uril in the Presence of Cations

The binding dynamics of R-(+)-2-naphthyl-1-ethylammonium cation (NpH(+)) with cucurbit[7]uril (CB[7]) was investigated. Competitive binding with Na(+) or H(3)O(+) cations enabled the reaction to be slowed down sufficiently for the kinetics to be studied by fluorescence stopped-flow experiments. The binding of two Na(+) cations to CB[7], i.e., CB[7]·Na(+) (K(01) = 130 ± 10 M(-1)) and Na(+)·CB[7]·Na(+) (K(02) = 21 ± 2 M(-1)), was derived from the analysis of binding isotherms and the kinetic studies. NpH(+) binds only to free CB[7] ((1.06 ± 0.05) × 10(7) M(-1)), and the association rate constant of (6.3 ± 0.3) × 10(8) M(-1) s(-1) is 1 order of magnitude lower than that for a diffusion-controlled process and much higher than the association rate constant previously determined for other CB[n] systems. The high equilibrium constant for the NpH(+)@CB[7] complex is a consequence of the slow dissociation rate constant of 55 s(-1). The kinetics results showed that formation of a complex between a positively charged guest with CB[n] can occur at a rate close to the diffusion-controlled limit with no detection of a stable exclusion complex.

On the Reactions of Methyl Radicals with TiO2 Nanoparticles and Granular Powders Immersed in Aqueous Solutions

Methyl radicals react with TiO(2) nanoparticles (NPs) immersed in aqueous solutions to form transients in which the methyls are covalently bound to the particles. The rate constant for this reaction approaches the diffusion-controlled limit and increases somewhat with the number of methyls bound to the particle. The transients decompose to yield ethane. Thus, formally the particles "catalyse" the dimerization of the radicals, a reaction that is diffusion-controlled. Rutile powders behave similarly to the TiO(2) NPs whereas the mechanism for the decomposition of the transients formed in the analogous reaction of the radicals with anatase powders differs. These results are of importance as alkyl radicals are formed near the surface of TiO(2) in a variety of important photocatalytic processes. The results imply that the reactions of alkyl radicals with TiO(2) have to be considered in these processes.

Nitration Activates Tyrosine toward Reaction with the Hydrated Electron

3-Nitrotyrosine has been reported as an important biomarker of oxidative stress that may play a role in a variety of diseases. In this work, transient UV-visible absorption spectra and kinetics observed during the reaction of the hydrated electron, e(aq)(-), with 3-nitrotyrosine and derivatives thereof were investigated. The absorption spectra show characteristics of aromatic nitro anion radicals. The absorptivity of radical anion product at 300 nm is estimated to be (1.0 ± 0.2) × 10(4) M(-1) cm(-1) at pH 7.3. The rate constants determined for the reaction of e(aq)(-) with 3-nitrotyrosine, N-acetyl-3-nitrotyrosine ethyl ester and glycylnitrotyrosylglycine at neutral pH (3.0 ± 0.3) × 10(10) M(-1) s(-1), (2.9 ± 0.2) × 10(10) M(-1) s(-1) and (1.9 ± 0.2) × 10(10) M(-1) s(-1), respectively, approach the diffusion-control limit and are almost two orders of magnitude higher than those for the reactions with tyrosine and tyrosine-containing peptides. The magnitude of the rate constants supports reaction of e(aq)(-) at the nitro group, and the product absorbance at 300 nm is consistent with formation of the nitro anion radical. The pH dependence of the second-order rate constant for e(aq)(-) decay (720 nm) in the presence of 3-nitrotyrosine shows a decrease with increasing pH, consistent with unfavorable electrostatic interactions. The pH dependence of the second-order rate constant for formation of radical anion (300 nm) product suggests that deprotonation of the amino group slows the rate, which indicates that deamination to form the 1-carboxy-2-(4-hydroxy-3-nitrophenyl)ethyl radical occurs. We conclude that the presence of the nitro group activates tyrosine and derivatives toward reaction with e(aq)(-) and can affect the redox chemistry of biomolecules exposed to oxidative stress.

Reaction between aminoalkyl radicals and akyl halides: Dehalogenation by electron transfer?

Aminoalkyl radicals, such as Et2NCHCH3, have low oxidation potentials and are therefore powerful reducing agents. We have found that Et2NCHCH3 reacts with CCl4 and CBr4 in di-tert-butyl peroxide with bimolecular rate constants (measured by LFP) close, or equal, to the diffusion-controlled limit. For the less reactive halide, CH2Br2, the reaction rate is increased substantially by the addition of acetonitrile as a co-solvent. It is tentatively concluded that these reactions occur by electron-transfer from the aminoalkyl to the organohalide with formation of the iminium ion, Et2N+CHCH3 (NMR detection), halide ion and a halomethyl radical, e.g., CCl3 and CHCl2 (ESR, spin-trapping detection).

Ionic Quenching of Naphthalene Fluorescence in Sodium Dodecyl Sulfate Micelles

Micellar effects on luminescense of organic compounds or probes are well established, and here we show that quenching is highly favored in aqueous sodium dodecyl sulfate (SDS) micelles, which concentrate a naphthalene probe and cations of lanthanides, transition metals, and noble metals. Interactions have been studied by steady state and time-resolved fluorescence in examining the fluorescence suppression of naphthalene by metal ions in anionic SDS micelles. The quenching is collisional and correlated with the unit charge and the reduction potential of the metal ion. The rate constants, calculated in terms of local metal ion concentrations, are close to the diffusion control limit in the interior of SDS micelles, where the microscopic viscosity decreases the transfer rate, following the Stokes-Einstein relation.

Coupling between homogeneous rate processes and fluid deformation rate: Brownian particle coagulation in a rapidly dilating solvent

AbstractP. Curie's principle applied to an isotropic medium of arbitrary EOS does not preclude coupling between homogeneous (chemical,…) rate processes and local fluid dilation rate. Yet, practical examples of this coupling have largely remained unexplored. Using recently studied supercritical “antisolvent” (SAS) examples for precipitating high‐value particles (e.g., pharmaceuticals), we suggest that the characteristic dilation time tV of the swelling solvent can be small enough to noticeably reduce the operative coagulation rate “constant,” β. Moreover, we expect that this coupling can occur under conditions in which postnucleation Brownian coagulation must be accounted for in predicting the efficacy of such micron‐sized powder production methods. Accordingly, a rational approximate theory for this rate constant “correction factor,” β/β(0), is proposed here, emphasizing the applicable limit of continuum Brownian diffusion control. We also present a preliminary assessment of the particle size distribution (PSD) consequences of these “corrections,” implying strategies to reduce both mean particle size and PSD spread. Possible generalizations are indicated. © 2010 American Institute of Chemical Engineers AIChE J, 2011

Multiparticle diffusion limited reaction in small volumes

A multiparticle reaction model in which particlesA annihilate inclusters of size k as is investigated analytically. The system is studied for arbitrary reaction orderk > 2, dimensiond, andsize L. Particles diffuse with diffusion constantD, and annihilate withrate σ which dependson the positions of kA particles in the cluster prior to a reaction. The particles are assumed to be spatially extended objects withradius a. Exclusion effects are not taken into account sinceA particles are allowed to overlap. The master equation is rephrased in the languageof a field theory which, in turn, is used to derive the equations of motion formany-point densities. An approximate form of the equations of motion was solvedanalytically in the diffusion-controlled limit (infinite reaction rate). An explicitexpression for the effective reaction rate has been found in the form of the Laplacetransform. It was shown that the number of particles saturates to a constantvalue for large times. The value is approached through an exponential decay.The exponential decay constant is the non-algebraic function of particle sizea and systemsize L.

ChemInform Abstract: Kinetics of the Reactions Between Alkyl Radicals and Molecular Oxygen in Aqueous Solution

The rate constant for the reaction R{sup {sm bullet}} + O{sub 2} {yields} ROO{sup {sm bullet}} in aqueous solution was determined for 18 alkyl radicals by laser flash photolysis. The values are all at the diffusion-controlled limit and lie in the range (1.6-4.9) {times} 10{sup 9} L mol{sup {minus}1} s{sup {minus}1}. The radicals studied are primary, substituted primary, secondary, and benzyl radicals.

ChemInform Abstract: Perfluorobutylperoxyl Radical as an Oxidant in Various Solvents.

Perfluorobutylperoxyl radicals were produced by pulse radiolysis of aerated solutions of perfluorobutyl iodide. The rate constants for reaction of this radical with several organic reductants, chlorpromazine, trolox, hydroquinone, and several other phenols, were determined in various solvents and were found to be in the range of 10{sup 5}-10{sup 9} M{sup {minus}1} s{sup {minus}1}. By comparison with other haloalkylperoxyl radicals, C{sub 4}F{sub 9}OO{sup {sm bullet}} was found to be a much more powerful oxidant, whose reactions took place more rapidly and were less sensitive to solvent and substituent effects. The rate constants (k) for oxidation of a series of para-substituted phenols by C{sub 4}F{sub 9}OO{sup {sm bullet}} gave a good linear correlation between log k and the electrophilic substituent constant {sigma}{sup +}, with a slope of {rho}{sup +} = {minus}2.3, indicating formation of a positively charged transition state. Parallel experiments with CCl{sub 3}OO{sup {sm bullet}} were limited to the most reactive phenols and gave a higher slope, {rho}{sup +} = {minus}3.3. The rates of reaction of C{sub 4}F{sub 9}OO{sup {sm bullet}} with trolox and chlorpromazine were found to depend on solvent viscosity, but much less on solvent polarity and acid-base properties, probably because they were closer to the diffusion-controlled limit. Themore » longer chain C{sub 10}F{sub 21}OO{sup {sm bullet}} was somewhat less reactive than C{sub 4}F{sub 9}OO{sup {sm bullet}} because of geometric factors.« less

Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and3D

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) modelof overdamped conservative dynamics, to address polymorphism, crystal nucleation, andcrystal growth in the diffusion-controlled limit. We refine the phase diagram for 3D, anddetermine the line free energy in 2D and the height of the nucleation barrier in 2Dand 3D for homogeneous and heterogeneous nucleation by solving the respectiveEuler–Lagrange (EL) equations. We demonstrate that, in the PFC model, thebody-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close-packedstructures (hcp) compete, while the simple cubic structure is unstable, and that phasepreference can be tuned by changing the model parameters: close to the critical point thebcc structure is stable, while far from the critical point the fcc prevails, with anhcp stability domain in between. We note that with increasing distance fromthe critical point the equilibrium shapes vary from the sphere to specific facetedshapes: rhombic dodecahedron (bcc), truncated octahedron (fcc), and hexagonalprism (hcp). Solving the equation of motion of the PFC model supplied withconserved noise, solidification starts with the nucleation of an amorphous precursorphase, into which the stable crystalline phase nucleates. The growth rate is foundto be time dependent and anisotropic; this anisotropy depends on the drivingforce. We show that due to the diffusion-controlled growth mechanism, which isespecially relevant for crystal aggregation in colloidal systems, dendritic growthstructures evolve in large-scale isothermal single-component PFC simulations. Anoscillatory effective pair potential resembling those for model glass formers has beenevaluated from structural data of the amorphous phase obtained by instantaneousquenching. Finally, we present results for eutectic solidification in a binary PFC model.

End-to-Surface Reaction Dynamics of a Single Surface-Attached DNA or Polypeptide

The dynamics of surface-attached polymers play a key role in the operation of a number of biological sensors, yet its current understanding is rather limited. Here we use computer simulations to study the dynamics of a reaction between the free end of a polymer chain and a surface, to which its other end has been attached. We consider two limiting cases, the diffusion-controlled limit, where the reaction is accomplished whenever the free chain end diffuses to within a specified distance from the surface, and the reaction-controlled limit, where slow, intrinsic reaction kinetics rather than diffusion of the chain is rate limiting. In the diffusion-controlled limit, we find that the overall rate scales as N(-b), where N is the number of monomers in the chain and b approximately = 2.2 for excluded volume chains. This value of the scaling exponent b is close to that derived from a simple approximate theory treating the dynamics of the chain end relative to the surface as one-dimensional diffusion in an effective potential. In the reaction-controlled limit, the value of the scaling exponent b is close to 1. We compare our findings with those for the related (and better studied) problem of end-to-end reactions within an unconstrained polymer chain and discuss their implications for electrochemical DNA sensors.

How Solvent Modulates Hydroxyl Radical Reactivity in Hydrogen Atom Abstractions

The hydroxyl radical (HO*) is a highly reactive oxygen-centered radical whose bimolecular rate constants for reaction with organic compounds (hydrogen atom abstraction) approach the diffusion-controlled limit in aqueous solution. The results reported herein show that hydroxyl radical is considerably less reactive in dipolar, aprotic solvents such as acetonitrile. This diminished reactivity is explained on the basis of a polarized transition state for hydrogen abstraction, in which the oxygen of the hydroxyl radical becomes highly negative and can serve as a hydrogen bond acceptor. Because acetonitrile cannot participate as a hydrogen bond donor, the transition state cannot be stabilized by hydrogen bonding, and the reaction rate is lower; the opposite is true when water is the solvent. This hypothesis explains hydroxyl radical reactivity both in solution and in the gas phase and may be the basis for a "containment strategy" used by Nature when hydroxyl radical is produced endogenously.

EPR Studies of the Generation, Structure, and Reactivity of N-Heterocyclic Carbene Borane Radicals

N-Heterocyclic carbene boranes (NHC-boranes) are a new "clean" class of reagents suitable for reductive radical chain transformations. Their structures are well suited for their reactivity to be tuned by inclusion of different NHC ring units and by appropriate placement of diverse substituents. EPR spectra were obtained for the boron-centered radicals generated on removal of one of the BH(3) hydrogen atoms. This spectroscopic data, coupled with DFT computations, demonstrated that the NHC-BH(2)* radicals are planar pi-delocalized species. tert-Butoxyl radicals abstracted hydrogen atoms from NHC-boranes more than 3 orders of magnitude faster than did C-centered radicals, although the rate decreased markedly for sterically shielded NHC-BH(3) centers. Combinations of two NHC-boryl radicals afforded 1,2-bis-NHC-diboranes at rates which also depended strongly on steric shielding. The termination rate increased to the diffusion-controlled limit for sterically unhindered NHC-boryls. Bromine atoms were rapidly transferred to imidazole-based NHC-boryl radicals from alkyl, allyl, and benzyl bromides. Chlorine-atom abstraction was, however, much less efficient and only observed for sterically unhindered NHC-boryls reacting with allylic and benzylic chlorides. For an NHC-borane containing a bulky thexyl substituent at boron, the tertiary H atom of the thexyl group was selectively removed. The resulting beta-boron-containing alkyl radical rapidly underwent beta scission of the B-C bond with production of an NHC-boryl radical and an alkene.

Reductive Fluorescence Quenching of the Photoexcited Free Base meso-Tetrakis (Pentafluorophenyl) Porphyrin by Amines

Steady state and time resolved fluorescence quenching behaviors of meso-Tetrakis (pentafluorophenyl) porphyrin (H(2)F(20)TPP) in presence of different aliphatic and aromatic amines have been executed in homogeneous dichloromethane (DCM) solution. At room temperature in DCM, free base (H(2)F(20)TPP) shows fluorescence with two distinct peaks at 640 and 711 nm and natural lifetime tauf=9.8 ns which are very similar to that of meso-tetraphenyl porphyrin (TPP). Unlike TPP, addition of both aliphatic and aromatic amines to a solution containing H(2)F(20)TPP results in an efficient decrease in fluorescence intensity without altering the shape and peak position of fluorescence emission. Upon addition of amines there was no change in optical absorption spectra of H(2)F(20)TPP. The fluorescence quenching rate constants ranged from 1 x 10(9) to 4 x 10(9) s(-1), which are one order below to the diffusion control limit, and temperature dependent quenching rate constants yield the activation energies which are found to be order of 0.1 eV. Femto second transient absorption studies reveal the existence of amine cation radical and porphyrin anion radicals with very short decay time (15 ps). The fluorescence quenching reaction follows Stern-Volmer kinetics. Steady state and time-resolved data are interpreted within general kinetic scheme of Marcus semi-classical model which attributes bimolecular electron transfer process between amines and the lowest excited singlet state of H(2)F(20)TPP. Calculated internal reorganization energies are found to be in between 0.04 and 0.22 ev. Variation of electron transfer rate as function of free energy change (DeltaG(0)) points the ET reactions in the present systems are in Marcus normal region. This is the first example of reductive fluorescence quenching of free base neutral porphyrins in homogeneous organic solvent ever known.

Spectroscopy and photoredox properties of soluble platinum(II) alkynyl complexes

A series of highly soluble platinum(II) alkynyl complexes with terdentate π-acceptor ligands was synthesized and investigated by optical spectroscopic and electrochemical means. Some of the new complexes are identified as viable alternatives to previously explored but poorly soluble platinum alkynyls that find use as sensitizers for photoredox reactions. Six complexes of platinum(II) with a terdentate π-acceptor ligand, 2,6-( N -( n -hexyl)benzimidazol-2′-yl)pyridine), and different ethynylbenzene ligands were synthesized and investigated by means of optical absorption, luminescence, and time-resolved emission spectroscopy. These complexes display similar photophysical and electrochemical properties as previously investigated analogs with the 2,2′:6′,2″-terpyridine ligand. The energy of the luminescence band maximum is a function of the nature of the chemical substituents attached to the ethynylbenzene ligand, luminescence intensities and lifetimes correlate with the luminescence wavelength according to the energy-gap law. The emissive excited states of some of these complexes are quenched reductively with efficiencies near the diffusion-controlled limit, even for moderate electron donors such as phenothiazine or triphenylamine. A complex with a dimethylamine substituent attached to the ethynylbenzene ligand exhibits photophysical properties that are strongly dependent on the protonation state of the amine. A dimer complex with a diethynyl-substituted xanthene bridging ligand displays absorption and emission behavior that is essentially identical to that of some of the monomeric platinum complexes investigated in this work. Short Pt(II)–Pt(II) contacts are only observed in the crystal structure of a precursor complex. A key feature of the new complexes is their good solubility in common organic solvents, thanks to the presence of two hexyl chains that are attached to the terdentate ligands.

The Rate of Intramolecular Loop Formation in DNA and Polypeptides: The Absence of the Diffusion-Controlled Limit and Fractional Power-Law Viscosity Dependence

The problem of determining the rate of end-to-end collisions for polymer chains has attracted the attention of theorists and experimentalists for more than three decades. The typical theoretical approach to this problem has focused on the case where a collision is defined as any instantaneous fluctuation that brings the chain ends to within a specific capture distance. In this paper, we study the more experimentally relevant case, where the end-to-end collision dynamics are probed by measuring the excited state lifetime of a fluorophore (or other lumiphore) attached to one chain end and quenched by a quencher group attached to the other end. Under this regime, a "contact" is defined not by the chain ends approach to within some sharp cutoff but, instead, typically by an exponentially distance-dependent process. Previous theoretical models predict that, if quenching is sufficiently rapid, a diffusion-controlled limit is attained, where such measurements report on the probe-independent, intrinsic end-to-end collision rate. In contrast, our theoretical considerations, simulations, and an analysis of experimental measurements of loop closure rates in single-stranded DNA molecules all indicate that no such limit exists, and that the measured effective collision rate has a nontrivial, fractional power-law dependence on both the intrinsic quenching rate of the fluorophore and the solvent viscosity. We propose a simple scaling formula describing the effective loop closure rate and its dependence on the viscosity, chain length, and properties of the probes. Previous theoretical results are limiting cases of this more general formula.

Singlet Oxygen Production upon Two‐Photon Excitation of TiO2 in Chloroform

Singlet oxygen ((1)O(2)) signals observed upon illumination at 532 nm are a consequence of TiO(2) excitation in a two-photon process, and at 355 nm in a one-photon pathway. After corrections for light reflectance, the relative quantum yields of (1)O(2) production are 0.23+/-0.01 and 0.22+/-0.02 for 532 and 355 nm excitation, respectively. Total quenching rate constants of (1)O(2) removal by TiO(2) particles are near the diffusion-controlled rate limit. By employing (1)O(2) as a probe, we have established an efficient and simple method to elucidate the nature of TiO(2) photoexcitation.

Packaging effects on site-specific DNA-protein interactions

We show that the rate of site-specific association of a protein molecule of interest with the DNA chain can be approximately 10(2) times higher than that of the three-dimensional diffusion-controlled collision rate limit approximately 10(8) mol(-1) s(-1) only when the protein molecule of interest searches for its specific site on the DNA chain in a reduced dimensional space with a dimensionality dr of dr<1. Upon considering the concurrent dynamics of the linear DNA chain that is embedded in a d-dimensional space along with the one-dimensional diffusion dynamics of the nonspecifically bound protein molecule on the DNA chain, we derive the generalized scaling law epsilon approximately 2(3(2-d)+3), where epsilon is the number of times by which the rate of site-specific association of the protein molecule with the DNA chain can be enhanced over the three-dimensional diffusion-controlled collision rate limit and d is the dimensionality of the reduced search space. Using the analogy between the self-intersection loop length in the theory of random walks and the ring-closure events in the theory of site specific interactions of a protein molecule with the DNA chain, we further show that the extent of packaging and volume compression of the genomic DNA inside the living cell is designed in such a way that the efficiency of the protein molecule in the process of searching for its specific site on the genomic DNA is a maximum. Our simulation results suggest that the volume compression factor theta which is the ratio between the total volume of the living cell and the volume occupied by the DNA chain along with all the other bound protein molecules should be such that theta>or=100 for an efficient site specific interaction of a protein molecule of interest with the linear DNA chain that is embedded in a three-dimensional space. Our theoretical and simulation results agree well with the E. coli cellular system.

Cyclometalated 6-Phenyl-2,2′-bipyridyl (CNN) Platinum(II) Acetylide Complexes: Structure, Electrochemistry, Photophysics, and Oxidative- and Reductive-Quenching Studies

Three cyclometalated 6-phenyl-4-(p-R-phenyl)-2,2'-bipyridyl (CNN-Ph-R) Pt(II) acetylide complexes, Pt(CNN-Ph-R)(CCPh), where R = Me (1), COOMe (2), and P(O)(OEt)(2) (3), have been synthesized and studied. Compounds 1 and 3 have been structurally characterized by single crystal X-ray crystallography and are found to exhibit distorted square planar geometries about the Pt(II) ions. The electrochemical properties of the compounds, as determined by cyclic voltammetry, have also been examined. Complexes 1-3 are brightly emissive in fluid CH(2)Cl(2) solution and in the solid state with lambda(em)(max) of ca. 600 nm and lifetimes on the order of ca. 500 ns in fluid solution. The emissions are assigned to a (3)MLCT transition. The complexes undergo oxidative quenching by MV(2+) with quenching rates near the diffusion-controlled limit (k(q) approximately 1.4 x 10(10) M(-1) s(-1)) in CH(2)Cl(2) solution. Reductive-quenching experiments of complexes 1-3 by the amine donors N,N,N',N'-tetramethylphenylenediamine (TMPD), phenothiazine (PTZ), and N,N,N',N'-tetramethylbenzidine (TMB) follow Stern-Volmer behavior, with very fast quenching rates on the order of 10(9)-10(10) M(-1) s(-1) in CH(2)Cl(2) solution. When the complexes are employed as the sensitizer in multiple component systems containing MV(2+), TEOA, and colloidal Pt in aqueous media, approximately one turnover of H(2) (TN vs mol of chromophore) is produced per hour upon irradiation with lambda > 410 nm but only after at least a 2 h induction period.

Fluorescence quenching of 9-cyanoanthracene in presence of zinc tetraphenylporphyrin in a polar liquid medium

Steady-state and time-resolved techniques are used to study photoinduced electron and/or excitational energy transfer processes involved within a novel donor (zinc tetraphenylporphyrin)–acceptor (9-cyanoanthracene) system in a polar liquid medium (acetonitrile) at the ambient temperature (300 K). After photoexcitation of 9-cyanoanthracene, its fluorescence emission as well as lifetime are found to be quenched in presence of zinc tetraphenylporphyrin. The fluorescence quenching is ascribed to be due to the combined effect of electron transfer from zinc tetraphenylporphyrin to 9-cyanoanthracene and energy transfer (radiative as well as non-radiative) from 9-cyanoanthracene to zinc tetraphenylporphyrin. The highly exergonic values of Gibbs free energy change for both forward electron transfer reaction (−1.15 eV) and charge recombination reaction (−1.94 eV) indicate the possibilities of occurrences of these two processes in the Marcus inverted region. The fluorescence quenching rate due to photoinduced electron transfer reaction is found to be close to the diffusion-controlled limit within the present donor–acceptor system upon excitation of the acceptor molecules.