Quantitative Modeling of Electron Dynamics and the Effect of Diffusion in Photosensitized Semiconductor Nanocomposites.

Photosensitized semiconducting nanomaterials have received considerable attention because of their applications in photocatalytic and photoelectronic devices. In such systems, photoexcited electrons with sufficiently high energies can be injected into the conduction band (CB) of an adjacent semiconductor. These excited electrons are subjected to various physical processes that can lead to their annihilation before exercising their catalytic/electric functions, and the efficiency of the photosensitized functions depends on the quantity of CB electrons produced and how long they remain near the surface region of the semiconductor. The rise and decay of photoexcited electrons in the semiconductor CB can be probed with transient IR absorption (TA), which was first demonstrated by Lian and co-workers. Results from various laboratories have since revealed that electrons appear in the CB following the excitation of the photosensitizer in tens to hundreds of femtoseconds and that the decay of the CB electrons typically exhibits multiple exponentials on varying ultrafast time scales. The size of the semiconductor nanoparticle appears to influence the diffusion of the CB electrons and thus their lifetimes. In all studies reported, the observed multiexponential decays have been analyzed and interpreted using purely phenomenological models, in which the individual decays were intuitively assigned to one specific relaxation or loss process. In reality, however, each exponential decay can be a convolution of multiple physical processes. In this Account, we report a universally applicable physical model, constructed by including all known electron dynamic processes, to quantitatively account for the multiexponential decays. We characterize the model as universal, as it can be used to analyze our own TA measurements, as well as data acquired in other laboratories. In our study of TiO2 nanorods photosensitized by Ag platelets, we demonstrate that each of the observed triple-exponential decays corresponds to a convolution of several physical decay processes occurring on similar time scales. The rate of each of the processes can be deconvoluted and determined to construct a complete, physically based model to assess the most important question: How many CB electrons are near the semiconductor surface region and what is their lifetime?The size of the semiconductor is an important consideration. Intuitively, as the semiconductor volume increases, there is more room for CB electrons to diffuse around, which increases their lifetime as annihilation occurs primarily at the surface. Indeed, Tachiya and co-workers previously reported that this lifetime increases with particle size. Nevertheless, while CB electrons live longer in the bulk of the particle, they are only useful when they are at the surface. Overall, what really matters is the CB electrons near the surface region, where the photosensitized functions actually occur. In applying our model to analyze the previously reported size-dependent Au/TiO2 results, we successfully reproduced the observation that larger semiconductor nanoparticles lengthen the lifetime of CB electrons because of diffusion into the bulk. More importantly, however, our model reveals that the size of the semiconductor has almost no influence on the retention of CB electrons near the semiconductor surface. This information is only revealed when all physical processes are quantitatively taken into account for the observed electron dynamics, which is not feasible with a phenomenological approach.

Collisional Relaxation of Highly Vibrationally Excited Acetylene Mediated by the Vinylidene Isomer.

Collisional relaxation of highly vibrationally excited acetylene, generated from the 193 nm photolysis of vinyl bromide with roughly 23,000 cm-1 of nascent vibrational energy, is studied via submicrosecond time-resolved Fourier transform infrared (FTIR) emission spectroscopy. IR emission from vibrationally hot acetylene during collisional relaxation by helium, neon, argon, and krypton rare-gas colliders is recorded and analyzed to deduce the acetylene energy content as a function of time. The average energy lost per collision, ⟨ΔE⟩, is computed using the Lennard-Jones collision frequency. Two distinct vibrational-to-translational (V-T) energy transfer regimes in terms of the acetylene energy are identified. At vibrational energies below 10,000-14,000 cm-1, energy transfer efficiency increases linearly with molecular energy content and is in line with typical V-T behavior in quantity. In contrast, above 10,000-14,000 cm-1, the V-T energy transfer efficiency displays a dramatic and rapid increase. This increase is nearly coincident with the acetylene-vinylidene isomerization limit, which occurs nearly 15,000 cm-1 above the acetylene zero-point energy. Combined quasi-classical trajectory calculations and Schwartz-Slawsky-Herzfeld-Tanczos theory point to a vinylidene contribution being responsible for the large enhancement. This observation illustrates the influence of energetically accessible structural isomers to greatly enhance the energy transfer rates of highly vibrationally excited molecules.

The low-lying electronic states and ultrafast relaxation dynamics of the monomers and J-aggregates of meso-tetrakis (4-sulfonatophenyl)-porphyrins.

The electronic and vibrational spectra of the meso-tetrakis(4-sulfonatophenyl)-porphyrins (TSPP) have been studied computationally using the PFD-3B functional with time-dependent density functional theory for the excited states. The calculated UV-vis absorption and emission spectra in aqueous solution are in excellent agreement with the experimental measurements of both H2TSPP-4 (monomer) at high pH and H4TSPP-2 (forming J-aggregate) at low pH. Moreover, our calculations reveal an infrared absorption at 1900 cm-1 in the singlet and triplet excited states that is absent in the ground state, which is chosen as a probe for transient IR absorption spectroscopy to investigate the vibrational dynamics of the excited state. Specifically, the S2 to S1 excited state internal conversion process time, the S1 state vibrational relaxation time, and the lifetime of the S1 excited electronic state are all quantitatively deduced.

Influence of intermolecular interactions on the infrared complex indices of refraction for binary liquid mixtures.

This paper investigates the accuracy of deriving the composite optical constants of binary mixtures from only the complex indices of refraction of the neat materials. These optical constants enable the reflectance spectra of the binary mixtures to be modeled for multiple scenarios (e.g., different substrates, thicknesses, volume ratios), which is important for contact and standoff chemical detection. Using volume fractions, each mixture's complex index of refraction was approximated via three different mixing rules. To explore the impact of intermolecular interactions, these predictions are tested by experimental measurements for two representative sets of binary mixtures: (1) tributyl phosphate combined with n-dodecane, a non-polar medium, to represent mixtures which primarily interact via dispersion forces and (2) tributyl phosphate and 1-butanol to represent mixtures with polar functional groups that can also interact via dipole-dipole interactions, including hydrogen bonding. The residuals and the root-mean-square error between the experimental and calculated index values are computed and demonstrate that for miscible liquids in which the average geometry of the cross-interactions can be considered isotropic (e.g., dispersion), the refractive indices of the mixtures can be modeled using composite n and k values derived from volume fractions of the neat liquids. Conversely, in spectral regions where the geometry of the cross-interactions is more restricted and anisotropic (e.g., hydrogen bonding), the calculated n and k values vary from the measured values. The impact of these interactions on the reflectance spectra are then compared by modeling a thin film of the binary mixtures on an aluminum substrate using both the measured and the mathematically computed indices of refraction.

Ag nanoplatelets as efficient photosensitizers for TiO2 nanorods.

The lifetime for injecting hot electrons generated in Ag nanoplatelets to nearby TiO2 nanorods was measured with ultrafast transient IR absorption to be 13.1 ± 1.5 fs, which is comparable to values previously reported for much smaller spherical Ag nanoparticles. Although it was shown that the injection rate decreases as the particle size increases, this observation can be explained by the facts that (1) the platelet has a much larger surface to bulk ratio and (2) the platelet affords a much larger surface area for direct contact with the semiconductor. These two factors facilitate strong Ag-TiO2 coupling (as indicated by the observed broadened surface plasmon resonance band of Ag) and can explain why Ag nanoplatelets have been found to be more efficient than much smaller Ag nanoparticles as photosensitizers for photocatalytic functions. The fast injection rate, together with a stronger optical absorption in comparison with Au and dye molecules, make Ag nanoplatelets a preferred photosensitizer for wide bandgap semiconductors.

Influence of Phase Transitions on Diffusive Molecular Transport Across Biological Membranes.

Phase transitions of lipid bilayer membranes should affect passive transport of molecules. While this hypothesis has been used to design drug-releasing thermosensitive liposomes, the effect has yet to be quantified. Herein, we use time-resolved second harmonic light scattering to measure transport of a molecular cation across membranes of unilamellar liposomes composed of the total lipid extract of E. coli from 9 °C to 36 °C, in which two distinct phase transitions (gel to liquid-disordered phase) have been identified. While the transport rate slowly increases with temperature as a diffusion process, dramatic jumps are observed at 14.7 °C and 27.6 °C, the known phase transitions. The transport rate constant measured as (7.3±0.8)×10-3  s-1 in the liquid-disordered phase at 36 °C is 35-times faster than (2.1±0.2)×10-4  s-1 of the gel phase at 9 °C. For the mixed-phase between these two phases, the measured rates are consistent with a structure of gel domains among a liquid-disordered bulk.

Determination of bacterial surface charge density via saturation of adsorbed ions.

Bacterial surface charge is a critical characteristic of the cell's interfacial physiology that influences how the cell interacts with the local environment. A direct, sensitive, and accurate experimental technique capable of quantifying bacterial surface charge is needed to better understand molecular adaptations in interfacial physiology in response to environmental changes. We introduce here the method of second-harmonic light scattering (SHS), which is capable of detecting the number of molecular ions adsorbed as counter charges on the exterior bacterial surface, thereby providing a measure of the surface charge. In this first demonstration, we detect the small molecular cation, malachite green, electrostatically adsorbed on the surface of representative strains of Gram-positive and Gram-negative bacteria. Surprisingly, the SHS-deduced molecular transport rates through the different cellular ultrastructures are revealed to be nearly identical. However, the adsorption saturation densities on the exterior surfaces of the two bacteria were shown to be characteristically distinct. The negative charge density of the lipopolysaccharide coated outer surface of Gram-negative Escherichia coli (6.6 ± 1.3 nm-2) was deduced to be seven times larger than that of the protein surface layer of Gram-positive Lactobacillus rhamnosus (1.0 ± 0.2 nm-2). The feasibility of SHS-deduced bacterial surface charge density for Gram-type differentiation is presented.

Control of Chemical Reactions through Coherent Excitation of Eigenlevels: A Demonstration via Vibronic Coupling in SO2.

Through coherent excitation of a pair of vibronically coupled eigenlevels, an oscillation of 130 kcal/mol in energy excitation between electronic and vibrational motions (on a time scale of 10-8 s) is created for the triatomic molecule, sulfur dioxide (SO2). The reactivity of the molecule can be influenced depending upon whether the molecule is vibrationally or electronically excited with this substantial amount of energy. The effect of excitation on reactivity is demonstrated through SO2 photodissociation as a function of time following coherent excitation, monitored by multiphoton ionization of the SO product.

Spatially Resolved Membrane Transport in a Single Cell Imaged by Second Harmonic Light Scattering.

We demonstrate that time-resolved second harmonic (SH) light scattering, when applied as an imaging modality, can be used to spatially resolve the adsorption and transport rates of molecules diffusing across the membrane in a living cell. As a representative example, we measure the passive transport of the amphiphilic ion, malachite green, across the plasma membrane in living human dermal fibroblast cells. Analysis of the time-resolved SH images reveals that membrane regions, which appear to be enduring higher stress, exhibit slower transport rates. It is proposed that this stress-transport relation may be a result of local enrichment of membrane rigidifiers as part of a response to maintain membrane integrity under strain.

Collisional Energy Transfer from Vibrationally Excited Hydrogen Isocyanide.

Collisional deactivation of vibrationally excited hydrogen isocyanide (HNC) by inert gas atoms was characterized using nanosecond time-resolved Fourier transform infrared emission spectroscopy. HNC, with an average nascent internal energy of 25.9 ± 1.4 kcal mol-1, was generated following the 193 nm photolysis of vinyl cyanide (CH2CHCN) and collisionally deactivated with the series of inert atomic gases: He, Ar, Kr, and Xe. Time-dependent IR emission allows simultaneous experimental observation of the ν1 NH and ν3 NC stretch emissions from vibrationally excited HNC. Subsequent spectral fit analysis enables direct determination of the average energy of HNC in each spectrum and therefore a measure of the average energy lost per collision, ⟨ΔE⟩, as a function of internal energy. Collisional deactivation of excited HNC is shown to be relatively efficient, exhibiting ⟨ΔE⟩ values more than an order of magnitude larger than comparably sized molecules at similar internal energies. Furthermore, the lighter inert gases are shown to be more efficient quenchers. Both observations can be qualitatively explained by the momentum gap law modeled through the repulsive force dominated vibration-to-translation energy transfer mechanism. The feasibility of efficient collisional deactivation as a contributing factor to the observed overabundance of astrophysical HNC is discussed.

Influence of molecular structure on passive membrane transport: A case study by second harmonic light scattering.

We present an experimental study, using the surface sensitive technique, second harmonic light scattering (SHS), to examine the influence of structure on the propensity of a molecule to passively diffuse across a phospholipid membrane. Specifically, we monitor the relative tendency of the structurally similar amphiphilic cationic dyes, malachite green (MG) and crystal violet (CV), to transport across membranes in living cells (E. coli) and biomimetic liposomes. Despite having nearly identical molecular structures, molecular weights, cationic charges, and functional groups, MG is of lower overall symmetry and consequently has a symmetry allowed permanent dipole moment, which CV does not. The two molecules showed drastically different interactions with phospholipid membranes. MG is observed to readily cross the hydrophobic interior of the bacterial cytoplasmic membrane. Conversely, CV does not. Furthermore, experiments conducted with biomimetic liposomes, constructed from the total lipid extract of E. coli and containing no proteins, show that while MG is able to diffuse across the liposome membrane, CV does not. These observations indicate that the SHS results measured with bacteria do not result from the functions of efflux pumps, but suggests that MG possesses an innate molecular property (which is absent in CV) that allows it to passively diffuse across the hydrophobic interior of a phospholipid membrane.

UV Photolysis of Pyrazine and the Production of Hydrogen Isocyanide.

Photolysis of the diazine heterocycle, pyrazine, following irradiation at 308, 248, and 193 nm was examined using nanosecond time-resolved Fourier transform infrared emission spectroscopy. The resulting time-resolved IR emission spectra reveal that for 308 and 248 nm vibrationally highly excited pyrazine is produced, but no photolysis products were detected. However, at 193 nm excitation, the measured IR emission spectra consist solely of resonances originating from rovibrationally excited photofragments, including acetylene (HCCH), hydrogen cyanide (HCN), and hydrogen isocyanide (HNC), indicating that photofragmentation proceeds from vibrationally highly excited pyrazine on the ground electronic state. Spectral fit analysis of the time-resolved HCN and HNC IR emission band shapes and intensities allowed an estimate of the nascent product population distributions, from which a lower bound estimate of the HNC/HCN branching ratio was deduced as Φ ≥ 0.07. Additionally, ab initio calculations were performed in order to examine the propensity of photoinduced reactions on the ground- and lowest-energy excited-state surfaces. The calculations provide a basis for understanding the wavelength dependence of the UV photolysis of pyrazine, the photolytic production of HNC, and also explain previous experimental observations in the literature.

Towards quantification of myelin by solid-state MRI of the lipid matrix protons.

PURPOSE: Direct assessment of myelin has the potential to reveal central nervous system abnormalities and serve as a means to follow patients with demyelinating disorders during treatment. Here, we investigated the feasibility of direct imaging and quantification of the myelin proton pool, without the many possible confounds inherent to indirect methods, via long-T2 suppressed 3D ultra-short echo-time (UTE) and zero echo-time (ZTE) MRI in ovine spinal cord. METHODS: ZTE and UTE experiments, with and without inversion-recovery (IR) preparation, were conducted in ovine spinal cords before and after D2O exchange of tissue water, on a 9.4T vertical-bore micro-imaging system, along with some feasibility experiments on a 3T whole-body scanner. Myelin density was quantified relative to reference samples containing various mass fractions of purified myelin lipid, extracted via the sucrose gradient extraction technique, and reconstituted by suspension in water, where they spontaneously self-assemble into an ensemble of multi-lamellar liposomes, analogous to native myelin. RESULTS: MR signal amplitudes from reference samples at 9.4T were linearly correlated with myelin concentration (R2 = 0.98-0.99), enabling their use in quantification of myelin fraction in neural tissues. An adiabatic inversion-recovery preparation was found to effectively suppress long-T2 water signal in white matter, leaving short-T2 myelin protons to be imaged. Estimated myelin lipid fractions in white matter were 19.9%-22.5% in the D2O-exchanged spinal cord, and 18.1%-23.5% in the non-exchanged spinal cord. Numerical simulations based on the myelin spectrum suggest that approximately 4.59% of the total myelin proton magnetization is observable by IR-ZTE at 3T due to T2 decay and the inability to excite the shortest T2* components. Approximately 380 µm of point-spread function blurring is predicted, and ZTE images of the spinal cord acquired at 3T were consistent with this estimate. CONCLUSION: In the present implementation, IR-UTE at 9.4T produced similar estimates of myelin concentration in D2O-exchanged and non-exchanged spinal cord white matter. 3T data suggest that direct myelin imaging is feasible, but remaining challenging on clinical MR systems.

Chemically Induced Changes to Membrane Permeability in Living Cells Probed with Nonlinear Light Scattering.

Second-harmonic light scattering (SHS) permits characterization of membrane-specific molecular transport in living cells. Herein, we demonstrate the use of time-resolved SHS for quantifying chemically induced enhancements in membrane permeability. As proof of concept, we examine the enhanced permeability of the cytoplasmic membrane in living Escherichia coli following addition of extracellular adenosine triphosphate (ATPe). The transport rate of the hydrophobic cation, malachite green, increases nearly an order of magnitude following addition of 0.1 mM ATPe. The absence of an ATPe-enhanced permeability in liposomes strongly suggests the induced effect is protein-mediated. The utility of SHS for elucidating the mechanism of action of antimicrobials is discussed.

Spectral reconstruction analysis for enhancing signal-to-noise in time-resolved spectroscopies.

We demonstrate a new spectral analysis for the enhancement of the signal-to-noise ratio (SNR) in time-resolved spectroscopies. Unlike the simple linear average which produces a single representative spectrum with enhanced SNR, this Spectral Reconstruction analysis (SRa) improves the SNR (by a factor of ca. 0.6√n) for all n experimentally recorded time-resolved spectra. SRa operates by eliminating noise in the temporal domain, thereby attenuating noise in the spectral domain, as follows: Temporal profiles at each measured frequency are fit to a generic mathematical function that best represents the temporal evolution; spectra at each time are then reconstructed with data points from the fitted profiles. The SRa method is validated with simulated control spectral data sets. Finally, we apply SRa to two distinct experimentally measured sets of time-resolved IR emission spectra: (1) UV photolysis of carbonyl cyanide and (2) UV photolysis of vinyl cyanide.

Direct magnetic resonance detection of myelin and prospects for quantitative imaging of myelin density.

Magnetic resonance imaging has previously demonstrated its potential for indirectly mapping myelin density, either by relaxometric detection of myelin water or magnetization transfer. Here, we investigated whether myelin can be detected and possibly quantified directly. We identified the spectrum of myelin in the spinal cord in situ as well as in myelin lipids extracted via a sucrose gradient method, and investigated its spectral properties. High-resolution solution NMR spectroscopy showed the extract composition to be in agreement with myelin's known chemical make-up. The 400-MHz (1)H spectrum of the myelin extract, at 20 °C (room temperature) and 37 °C, consists of a narrow water resonance superimposed on a broad envelope shifted ∼3.5 ppm upfield, suggestive of long-chain methylene protons. Superimposed on this signal are narrow components resulting from functional groups matching the chemical shifts of the constituents making up myelin lipids. The spectrum could be modeled as a sum of super-Lorentzians with a T(2)* distribution covering a wide range of values (0.008-26 ms). Overall, there was a high degree of similarity between the spectral properties of extracted myelin lipids and those found in neural tissue. The normalized difference spectrum had the hallmarks of membrane proteins, not present in the myelin extract. Using 3D radially ramp-sampled proton MRI, with a combination of adiabatic inversion and echo subtraction, the feasibility of direct myelin imaging in situ is demonstrated. Last, the integrated signal from myelin suspensions is shown, both spectroscopically and by imaging, to scale with concentration, suggesting the potential for quantitative determination of myelin density.

Chemical activation through super energy transfer collisions.

Can a molecule be efficiently activated with a large amount of energy in a single collision with a fast atom? If so, this type of collision will greatly affect molecular reactivity and equilibrium in systems where abundant hot atoms exist. Conventional expectation of molecular energy transfer (ET) is that the probability decreases exponentially with the amount of energy transferred, hence the probability of what we label "super energy transfer" is negligible. We show, however, that in collisions between an atom and a molecule for which chemical reactions may occur, such as those between a translationally hot H atom and an ambient acetylene (HCCH) or sulfur dioxide, ET of chemically significant amounts of energy commences with surprisingly high efficiency through chemical complex formation. Time-resolved infrared emission observations are supported by quasi-classical trajectory calculations on a global ab initio potential energy surface. Results show that ∼10% of collisions between H atoms moving with ∼60 kcal/mol energy and HCCH result in transfer of up to 70% of this energy to activate internal degrees of freedom.

Observing mechanosensitive channels in action in living bacteria.

Mechanosensitive (MS) channels act to protect the cytoplasmic membrane (CM) of living cells from environmental changes in osmolarity. In this report, we demonstrate the use of time-resolved second-harmonic light scattering (SHS) as a means of experimentally observing the relative state (open versus closed) of MS channels in living bacteria suspended in different buffer solutions. Specifically, the state of the MS channels was selectively controlled by changing the composition of the suspension medium, inducing either a transient or persistent osmotic shock. SHS was then used to monitor transport of the SHG-active cation, malachite green, across the bacterial CM. When MS channels were forced open, malachite green cations were able to cross the CM at a rate at least two orders of magnitude faster compared with when the MS channels were closed. These observations were corroborated using both numerical model simulations and complementary fluorescence experiments, in which the propensity for the CM impermeant cation, propidium, to stain cells was shown to be contingent upon the relative state of the MS channels (i.e., cells with open MS channels fluoresced red, cells with closed MS channels did not). Application of time-resolved SHS to experimentally distinguish MS channels opened via osmotic shock versus chemical activation, as well as a general comparison with the patch-clamp method is discussed.

Optimal Spectral Resolution for Infrared Studies of Solids and Liquids.

Due to a legacy originating in the limited capability of early computers, the spectroscopic resolution used in Fourier transform infrared spectroscopy and other systems has largely been implemented using only powers of two for more than 50 years. In this study, we investigate debunking the spectroscopic lore of, e.g., using only 2, 4, 8, or 16 cm-1 resolution and determine the optimal resolution in terms of both (i) a desired signal-to-noise ratio and (ii) efficient use of acquisition time. The study is facilitated by the availability of solids and liquids reference spectral data recorded at 2.0 cm-1 resolution and is based on an examination in the 4000-400 cm-1 range of 61 liquids and 70 solids spectra, with a total analysis of 4237 peaks, each of which was also examined for being singlet/multiplet in nature. Of the 1765 liquid bands examined, only 27 had widths <5 cm-1. Of the 2472 solid bands examined, only 39 peaks have widths <5 cm-1. For both the liquid and solid bands, a skewed distribution of peak widths was observed: For liquids, the mean peak width was 24.7 cm-1 but the median peak width was 13.7 cm-1, and, similarly, for solids, the mean peak width was 22.2 cm-1 but the median peak width was 11.2 cm-1. While recognizing other studies may differ in scope and limiting the analysis to only room temperature data, we have found that a resolution to resolve 95% of all bands is 5.7 cm-1 for liquids and 5.3 cm-1 for solids; such a resolution would capture the native linewidth (not accounting for instrumental broadening) for 95% of all the solids and liquid bands, respectively. After decades of measuring liquids and solids at 4, 8, or 16 cm-1 resolution, we suggest that, when accounting only for intrinsic linewidths, an optimized resolution of 6.0 cm-1 will capture 91% of all condensed-phase bands, i.e., broadening of only 9% of the narrowest of bands, but yielding a large gain in signal-to-noise with minimal loss of specificity.

Photolysis (193 nm) of SO2: nascent product energy distribution examined through IR emission.

Infrared emission following the photolysis of SO(2) by a 193 nm laser pulse (20 ns duration) was recorded with 500 ns time and 10 cm(-1) spectral resolution. Spectral analyses of the time-resolved spectra revealed the vibrationally excited nascent SO population distribution as (v = 1)/(v = 2)/(v = 3)/(v = 4)/(v = 5) = 0.54 ± 0.04, 1.00 ± 0.03, 0.00 ± 0.03, 0.01 ± 0.03, and 0.10 ± 0.03. The nascent SO was found to be rotationally excited with an average rotational temperature around 1000 K for v = 1 and v = 2 levels and 300 K for the v = 5 level. The vibrationally excited SO likely originates from two distinct dissociation mechanisms; the v = 1 and 2 populations are generated through intersystem crossing between the C state and a repulsive state (2(3)A'), and the v = 5 population is generated through internal conversion from the C to the X state. Efficient V-V energy transfer from nascent vibrationally excited SO to SO(2)(ν(1)) is also observed. The appearance of the SO(2)(ν(1)) ν(1) = 2 emission, before that from the ν(1) = 1 population is consistent with the previous report that the Δν = -2 channel is more efficient than the Δν = -1 channel.