*J Chem Theory Comput ; 2020 Mar 26.*

**| MEDLINE**| ID: mdl-32212729

##### RESUMO

An efficient method is described for generating a fragmented, permutationally invariant polynomial basis to fit electronic energies and, if available, gradients for large molecules. The method presented rests on the fragmentation of a large molecule into any number of fragments while maintaining the permutational invariance and uniqueness of the polynomials. The new approach improves on a previous one reported by Qu and Bowman by avoiding repetition of polynomials in the fitting basis set and speeding up gradient evaluations while keeping the accuracy of the PES. The method is demonstrated for CH3-NH-CO-CH3 (N-methyl acetamide) and NH2-CH2-COOH (glycine).

*J Phys Chem A ; 123(46): 9957-9965, 2019 Nov 21.*

**| MEDLINE**| ID: mdl-31661966

##### RESUMO

The H atom product channels in the ultraviolet photodissociation of 2-propenyl (CH2CCH3) radical were investigated in the wavelength region 224-248 nm using photofragment translational spectroscopy. The CH2CCH3 radicals were generated by 193 nm photodissociation of 2-chloropropene and 2-bromopropene precursors. The H atom photofragment yield spectra from both precursors revealed a broad feature peaking near 232 nm. The translational energy distributions of the H + C3H4 products peaked around 7-8 kcal/mol and extended close to the maximum excess energy. The fraction of the total available energy released as products' translation was nearly a constant (â¼0.16 using the 2-chloropropene precursor and â¼0.18 using the 2-bromopropene precursor) in the wavelength range 224-248 nm. The angular distribution of the H atom product was isotropic. Quasi-classical trajectory (QCT) calculations were performed on the ground-state potential energy surface of CH2CCH3 for its decomposition at a 124 kcal/mol excitation energy (equivalent to 230 nm photolysis photon energy). The calculations yielded branching ratios for different dissociation product channels, 32% H + allene, 35% H + propyne, 0.5% H + cyclopropene, and 32% methyl + acetylene. The experimental and QCT translational energy distributions of the H atom loss channels qualitatively agreed, consistent with the main H atom product channels being the H + allene and H + propyne dissociations. The time scale of the 2-propenyl dissociation on the ground electronic state was calculated to be â¼2 ps, smaller compared to that of the overall UV photodissociation (≥10 ps, implied on the basis of the isotropic H atom product angular distribution). The mechanism of the UV photodissociation of 2-propenyl is consistent with unimolecular dissociation proceeding on the ground electronic state after internal conversion of the electronic excited states.

*J Phys Chem Lett ; : 5250-5258, 2019 Aug 26.*

**| MEDLINE**| ID: mdl-31423788

##### RESUMO

We report a machine learning approach to train and predict bimolecular thermal rate constants over a large temperature range. The approach uses Gaussian process (GP) regression to evaluate the difference between accurate quantum results and Eckart-corrected conventional transition state theory, mostly for collinear reactions. Training is done on a database of rate constants for 13 reaction/potential surface combinations, and testing is performed on a set of 39 reaction/potential surface combinations. Averaged over all test reactions, the GP method is within 80% of the accurate answer, whereas transition state theory (TST) is only within 330% and Eckart-corrected TST (ECK) is within 110%. In the tunneling region, GP is generally (with a few exceptions) more accurate and sometimes much more accurate. In the high-temperature recrossing region, GP is significantly more accurate than either TST or ECK, neither of which addresses the possibility of recrossing. The GP predictions for the 3D reactions O(3P) + H2, OH + H2, O(3P) + CH4, and H + CH4, for which accurate quantum results are available, provide further encouragement to the machine learning approach.

*Faraday Discuss ; 212(0): 65-82, 2018 12 13.*

**| MEDLINE**| ID: mdl-30259026

##### RESUMO

A new paradigm for assigning vibrational spectra is described. Instead of proceeding from potential to Hamiltonian to eigenvalues/eigenvectors/intensities to spectrum, the new method goes "backwards" directly from spectrum to eigenvectors. The eigenvectors then "assign" the spectrum, in that they identify the basis states that contribute to each eigenvalue. To start, we demonstrate an algorithm that can obtain useful estimates of the eigenvectors connecting a real, symmetric Hamiltonian to its eigenvalues even if the only available information about the Hamiltonian is its diagonal elements. When this algorithm is augmented with information about transition intensities, it can be used to assign a complex vibrational spectrum using only information about (1) eigenvalues (the peak centers of the spectrum) and (2) a harmonic basis set (taken to be the diagonal elements of the Hamiltonian). Examples will be discussed, including application to the vibrationally complex spectral region of the formic acid dimer.

*Chem Soc Rev ; 46(24): 7615-7624, 2017 Dec 11.*

**| MEDLINE**| ID: mdl-28979955

##### RESUMO

The phenomenon of roaming in chemical reactions has now become both commonly observed in experiment and extensively supported by theory and simulations. Roaming occurs in highly-excited molecules when the trajectories of atomic motion often bypass the minimum energy pathway and produce reaction in unexpected ways from unlikely geometries. The prototypical example is the unimolecular dissociation of formaldehyde (H2CO), in which the "normal" reaction proceeds through a tight transition state to yield H2 + CO but for which a high fraction of dissociations take place via a "roaming" mechanism in which one H atom moves far from the HCO, almost to dissociation, and then returns to abstract the second H atom. We review below the theories and simulations that have recently been developed to address and understand this new reaction phenomenon.

*J Chem Phys ; 147(1): 013936, 2017 Jul 07.*

**| MEDLINE**| ID: mdl-28688379

##### RESUMO

The photodissociation dynamics of roaming in formaldehyde are studied by comparing quasi-classical trajectory calculations performed on a new potential energy surface (PES) to new and detailed experimental results detailing the CO + H2 product state distributions and their correlations. The new PES proves to be a significant improvement over the past one, now more than a decade old. The new experiments probe both the CO and H2 products of the formaldehyde dissociation. The experimental and trajectory data offer unprecedented detail about the correlations between internal states of the CO and H2 dissociation products as well as information on how these distributions are different for the roaming and transition-state pathways. The data investigated include, for dissociation on the formaldehyde 2143 band, (a) the speed distributions for individual vibrational/rotational states of the CO products, providing information about the correlated internal energy distributions of the H2 product, and (b) the rotational and vibrational distributions for the CO and H2 products as well as the contributions to each from both the transition state and roaming channels. The agreement between the trajectory and experimental data is quite satisfactory, although minor differences are noted. The general agreement provides support for future use of the experimental techniques and the new PES in understanding the dynamics of photodissociative processes.

*J Chem Phys ; 147(1): 013601, 2017 Jul 07.*

**| MEDLINE**| ID: mdl-28688442

##### RESUMO

Since the first ion imaging experiment [D. W. Chandler and P. L. Houston, J. Chem. Phys. 87, 1445-1447 (1987)], demonstrating the capability of collecting an image of the photofragments from a unimolecular dissociation event and analyzing that image to obtain the three-dimensional velocity distribution of the fragments, the efficacy and breadth of application of the ion imaging technique have continued to improve and grow. With the addition of velocity mapping, ion/electron centroiding, and slice imaging techniques, the versatility and velocity resolution have been unmatched. Recent improvements in molecular beam, laser, sensor, and computer technology are allowing even more advanced particle imaging experiments, and eventually we can expect multi-mass imaging with co-variance and full coincidence capability on a single shot basis with repetition rates in the kilohertz range. This progress should further enable "complete" experiments-the holy grail of molecular dynamics-where all quantum numbers of reactants and products of a bimolecular scattering event are fully determined and even under our control.

*Philos Trans A Math Phys Eng Sci ; 375(2092)2017 Apr 28.*

**| MEDLINE**| ID: mdl-28320899

##### RESUMO

We report a new global potential energy surface (PES) for H2CO, based on precise fitting of roughly 67 000 MRCI/cc-pVTZ energies. This PES describes the global minimum, the cis- and trans-HCOH isomers, and barriers relevant to isomerization, formation of the molecular (H2+CO) and radical (H+HCO) products, and the loose so-called roaming transition-state saddle point. The key features of the PES are reviewed and compared with a previous PES, denoted by PES04, based on five local fits that are 'stitched' together by switching functions (Zhang et al. 2004 J. Phys. Chem. A108, 8980-8986 (doi:10.1021/jp048339l)). Preliminary quasi-classical trajectory calculations are performed at the total energy of 36 233 cm-1 (103 kcal mol-1), relative to the H2CO global minimum, using the new PES, with a particular focus on roaming dynamics. When compared with the results from PES04, the new PES findings show similar rotational distributions, somewhat more roaming and substantially higher H2 vibrational excitation.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

*J Phys Chem A ; 120(27): 5248-56, 2016 Jul 14.*

**| MEDLINE**| ID: mdl-26963771

##### RESUMO

Ultraviolet (UV) photodissociation dynamics of jet-cooled 1-propenyl radical (CHCHCH3) were investigated at the photolysis wavelengths from 224 to 248 nm using high-n Rydberg atom time-of-flight (HRTOF) technique. The 1-propenyl radicals were produced from 193 nm photolysis of 1-chloropropene and 1-bromopropene precursors. The photofragment yield (PFY) spectra of the H atom product have a broad peak centered at 230 nm. The H + C3H4 product translational energy P(ET) distribution's peak near â¼8 kcal/mol, and the fraction of average translational energy in the total available energy, ⟨fT⟩, is nearly a constant of â¼0.12 from 224 to 248 nm. The H atom product has an isotropic angular distribution with the anisotropy parameter ß ≈ 0. Quasiclassical trajectory calculations were also carried out using an ab initio ground-state potential energy surface for dissociation of 1-propenyl at the excitation energy of 124 kcal/mol (230 nm). The calculated branching ratios are 60% to the methyl + acetylene products, 16% to H + propyne, 4% to H + allene, and 1% to H + cyclopropene. The experimental and calculated P(ET) distributions of the H + C3H4 products at 230 nm are in a qualitative agreement, suggesting that the H + propyne dissociation is the main H atom product channel. The calculated dissociation time scale on the ground electronic state is â¼1 ps, shorter than but close to the time scale of >10 ps for the overall UV photodissociation implied by the isotropic H atom product angular distribution. The UV photodissociation mechanism of 1-propenyl can be described as unimolecular decomposition of hot 1-propenyl radical on the ground electronic state following internal conversion from the electronically excited states of 1-propenyl.

*J Phys Chem A ; 120(27): 5103-14, 2016 Jul 14.*

**| MEDLINE**| ID: mdl-26885745

##### RESUMO

The photodissociation of formaldehyde was studied using quasi-classical trajectories to investigate "roaming," or events involving trajectories that proceed far from the minimum energy pathway. Statistical analysis of trajectories performed over a range of nine excitation energies from 34â¯500 to 41â¯010 cm(-1) (including zero-point energy) provides characterization of the roaming phenomenon and insight into the mechanism. The trajectories are described as projections onto three coordinates: the distance from the CO center of mass to the furthest H atom and the azimuthal and polar coordinates of that H atom with respect to the CO axis. The trajectories are used to construct a "minimum energy" potential energy surface showing the potential for any binary combination of these three coordinates that is at a minimum energy with respect to values of the other coordinates encountered during the trajectories. We also construct flux diagrams for roaming, transition-state, and radical pathways, as well as "reaction configuration" plots that show the distribution of reaction geometries for roaming and transition-state pathways. These constructs allow characterization of roaming in formaldehyde as, principally, internal rotation of the roaming H atom around the CO axis at a slowly varying and elongated distance from the CO center of mass. The rotation is nearly uniform, and is sometimes accompanied by rotation in the polar coordinate. The roaming state of formaldehyde can be treated as a separate kinetic entity, much as one might treat an isomer. Rate constants for the formation of and reaction from this roaming state are derived from the trajectory data as a function of excitation energy.

*J Phys Chem A ; 119(50): 12304-17, 2015 Dec 17.*

**| MEDLINE**| ID: mdl-26299678

##### RESUMO

Quasi-classical trajectory studies have been performed for the collision of internally excited methane with water using an accurate methane-water potential based on a full-dimensional, permutationally invariant analytical representation of energies calculated at a high level of theory. The results suggest that most energy transfer takes place at impact parameters smaller than about 8 Bohr; collisions at higher impact parameters are mostly elastic. Overall, energy transfer is fairly facile, with values for ⟨ΔEdown⟩ and ⟨ΔEup⟩ approaching almost 2% of the total excitation energy. A classical model previously developed for the collision of internally excited molecules with atoms (Houston, P. L.; Conte, R.; Bowman, J. M. J. Phys. Chem. A 2015, 119, 4695-4710) has been extended to cover collisions of internally excited molecules with other molecules. For high initial rotational levels, the agreement with the trajectory results is quite good (R(2) ≈ 0.9), whereas for low initial rotational levels it is only fair (R(2) ≈ 0.7). Both the model and the trajectories can be characterized by a four-dimensional joint probability distribution, P(J1,f,ΔE1,J2,f,ΔE2), where J1,f and J2,f are the final rotational levels of molecules 1 and 2 and ΔE1 and ΔE2 are the respective changes in internal energy. A strong anticorrelation between ΔE1 and ΔE2 is observed in both the model and trajectory results and can be explained by the model. There is evidence in the trajectory results for a small amount of V â V energy transfer from the water, which has low internal energy, to the methane, which has substantial internal energy. This observation suggests that V â V energy transfer in the other direction also occurs.

*J Phys Chem A ; 119(20): 4695-710, 2015 May 21.*

**| MEDLINE**| ID: mdl-25907301

##### RESUMO

A model for energy transfer in the collision between an atom and a highly excited target molecule has been developed on the basis of classical mechanics and turning point analysis. The predictions of the model have been tested against the results of trajectory calculations for collisions of five different target molecules with argon or helium under a variety of temperatures, collision energies, and initial rotational levels. The model predicts selected moments of the joint probability distribution, P(Jf,ΔE) with an R(2) ≈ 0.90. The calculation is efficient, in most cases taking less than one CPU-hour. The model provides several insights into the energy transfer process. The joint probability distribution is strongly dependent on rotational energy transfer and conservation laws and less dependent on vibrational energy transfer. There are two mechanisms for rotational excitation, one due to motion normal to the intermolecular potential and one due to motion tangential to it and perpendicular to the line of centers. Energy transfer is found to depend strongly on the intermolecular potential and only weakly on the intramolecular potential. Highly efficient collisions are a natural consequence of the energy transfer and arise due to collisions at "sweet spots" in the space of impact parameter and molecular orientation.

*Phys Chem Chem Phys ; 17(12): 8172-81, 2015 Mar 28.*

**| MEDLINE**| ID: mdl-25726765

##### RESUMO

The potential energy surface of the methane-water dimer is represented as the sum of a new intrinsic two-body potential energy surface and pre-existing intramolecular potentials for the monomers. Different fits of the CH4-H2O intrinsic two-body energy are reported. All these fits are based on 30 467 ab initio interaction energies computed at CCSD(T)-F12b/haTZ (aug-cc-pVTZ for C and O, cc-pVTZ for H) level of theory. The benchmark fit is a full-dimensional, permutationally-invariant analytical representation with root-mean-square (rms) fitting error of 3.5 cm(-1). Two other computationally more efficient two-body potentials are also reported, albeit with larger rms fitting errors. Of these a compact permutationally invariant fit is shown to be the best one in combining precision and speed of evaluation. An intrinsic two-body dipole moment surface is also obtained, based on MP2/haTZ expectation values, with an rms fitting error of 0.002 au. As with the potential, this dipole moment surface is combined with existing monomer ones to obtain the full surface. The vibrational ground state of the dimer and dissociation energy, D0, are determined by diffusion Monte Carlo calculations, and MULTIMODE calculations are performed for the IR spectrum of the intramolecular modes. The relative accuracy of the different intrinsic two-body potentials is analyzed by comparing the energetics and the harmonic frequencies of the global minimum well, and the maximum impact parameter employed in a sample methane-water scattering calculation.

*J Phys Chem A ; 118(36): 7742-57, 2014 Sep 11.*

**| MEDLINE**| ID: mdl-25116695

##### RESUMO

The influence of rotational excitation on energy transfer in single collisions of allyl with argon and on allyl dissociation is investigated. About 90,000 classical scattering simulations are performed in order to determine collision-induced changes in internal energy and in allyl rotational angular momentum. Dissociation is studied by means of about 50,000 additional trajectories evolved for the isolated allyl under three different conditions: allyl with no angular momentum (J = 0); allyl with the same microcanonically sampled initial conditions used for the collisions (J*); allyl evolving from the corresponding exit conditions after the collision. The potential energy surface is the sum of an intramolecular potential and an interaction one, and it has already been used in a previous work on allyl-argon scattering (Conte, R.; Houston, P. L.; Bowman, J. M. J. Phys. Chem. A 2013, 117, 14028-14041). Energy transfer data show that increased initial rotation favors, on average, increased relaxation of the excited molecule. The availability of a high-level intramolecular potential energy surface permits us to study the dependence of energy transfer on the type of starting allyl isomer. A turning point analysis is presented, and highly efficient collisions are detected. Collision-induced variations in the allyl rotational angular momentum may be quite large and are found to be distributed according to three regimes. The roles of rotational angular momentum, collision, and type of isomer on allyl unimolecular dissociation are considered by looking at dissociations times, kinetic energies of the fragments, and branching ratios. Generally, rotational angular momentum has a strong influence on the dissociation dynamics, while the single collision and the type of starting isomer are less influential.

*J Phys Chem A ; 118(36): 7758-75, 2014 Sep 11.*

**| MEDLINE**| ID: mdl-25116732

##### RESUMO

The excitation/de-excitation step in the Lindemann mechanism is investigated in detail using model development and classical trajectory studies based on a realistic potential energy surface. The model, based on a soft-sphere/line-of-centers approach and using elements of Landau-Teller theory and phase space theory, correctly predicts most aspects of the joint probability distribution P(ΔE,ΔJ) for the collisional excitation and de-excitation process in the argon-allyl system. The classical trajectories both confirm the validity of the model and provide insight into the energy transfer. The potential employed was based on a previously available ab initio intramolecular potential for the allyl fit to 97418 allyl electronic energies and an intermolecular potential fit to 286 Ar-allyl energies. Intramolecular energies were calculated at the CCSD(T)/AVTZ level of theory, while intermolecular energies were calculated at the MP2/AVTZ level of theory. Trajectories were calculated for each of four starting allyl isomers and for an initial rotational level of Ji = 0 as well as for Ji taken from a microcanonical distribution. Despite a dissimilarity in Ar-allyl potentials for fixed Ar-allyl geometries, energy transfer properties starting from four different isomers were found to be remarkably alike. A contributing factor appears to be that the orientation-averaged potentials are almost identical. The model we have developed suggests that most hydrocarbons should have similar energy transfer properties, scaled by differences in the potential offset of the atom-hydrogen interaction. Available data corroborate this suggestion.

*J Phys Chem A ; 117(51): 14028-41, 2013 Dec 27.*

**| MEDLINE**| ID: mdl-24299271

##### RESUMO

Predicting the results of collisions of polyatomic molecules with a bath of atoms is a research area that has attracted substantial interest in both experimental and theoretical chemistry. Energy transfer, which is the consequence of such collisions, plays an important role in gas-phase kinetics and relaxation of excited molecules. We present a study of energy transfer in single collisions of highly vibrationally excited allyl radical in argon. We evolve a total of 52 000 classical trajectories on a potential energy surface, which is the sum of an ab initio intramolecular potential for the allyl and a pairwise interaction potential describing the argon's effect on the allyl. The former is described by means of a permutationally invariant full-dimensional potential, whereas the interaction potential between allyl and argon is obtained by means of a sum of pairwise potentials dependent on nonlinear parameters that have been fit to a set of MP2/avtz counterpoise corrected ab initio energies. Results are reported for energy transfers and related probability densities at different collisional energies. The sensitivity of results to the interaction potential is considered and the potential is shown to be suitable for future applications involving different isomers of the allyl. The impact of highly efficient collisions in the energy transfer process is examined.

*J Phys Chem A ; 115(25): 6797-804, 2011 Jun 30.*

**| MEDLINE**| ID: mdl-21696213

##### RESUMO

Dissociation of the allyl radical, CH(2)CHCH(2), and its deuterated isotopolog, CH(2)CDCH(2), have been investigated using trajectory calculations on an ab initio ground-state potential energy surface calculated for 97,418 geometries at the coupled cluster single and double and perturbative treatment of triple excitations, with the augmented correlation consistent triple-Î¶ basis set level (CCSD(T)/AVTZ). At an excitation energy of 115 kcal/mol, corresponding to optical excitation at 248 nm, the primary channel is hydrogen loss with a quantum yield of 0.94 to give either allene or propyne in a ratio of 6.4:1. The total dissociation rate for CH(2)CHCH(2) is 6.3 × 10(10) s(-1), corresponding to a 1/e time of 16 ps. Methyl and C(2)H(2) are produced with a quantum yield of 0.06 by three different mechanisms: a 1,3 hydrogen shift followed by C-C cleavage to give methyl and acetylene, a double 1,2 shift followed by C-C cleavage to give methyl and acetylene, or a single 1,2 hydrogen shift followed by C-C cleavage to give methyl and vinylidene. In this last channel, the vinylidene eventually isomerizes to give internally excited acetylene, and the kinetic energy distribution is peaked at much lower energy (6.4 kcal/mol) than that for the other two channels (18 kcal/mol). The trajectory results also predict the v-J correlation, the anisotropy of dissociation, and distributions for the angular momentum of the fragments. The v-J correlation for the CH(3) + HCCH channel is strongest for high rotational levels of acetylene, where v is perpendicular to J. Methyl elimination is anisotropic, with ß = 0.66, whereas hydrogen elimination is nearly isotropic. In the hydrogen elimination channel, allene is rotationally excited with a total angular momentum distribution peaked near J = 17. In the methyl elimination channel, the peak of the methyl rotational distribution is at J ≈ 12, whereas the peak of the acetylene rotational distribution is at J ≈ 28.

*Appl Environ Microbiol ; 75(23): 7426-35, 2009 Dec.*

**| MEDLINE**| ID: mdl-19801466

##### RESUMO

Attached bacterial communities can generate three-dimensional (3D) physicochemical gradients that create microenvironments where local conditions are substantially different from those in the surrounding solution. Given their ubiquity in nature and their impacts on issues ranging from water quality to human health, better tools for understanding biofilms and the gradients they create are needed. Here we demonstrate the use of functional tomographic imaging via confocal fluorescence microscopy of ratiometric core-shell silica nanoparticle sensors (C dot sensors) to study the morphology and temporal evolution of pH microenvironments in axenic Escherichia coli PHL628 and mixed-culture wastewater biofilms. Testing of 70-, 30-, and 10-nm-diameter sensor particles reveals a critical size for homogeneous biofilm staining, with only the 10-nm-diameter particles capable of successfully generating high-resolution maps of biofilm pH and distinct local heterogeneities. Our measurements revealed pH values that ranged from 5 to >7, confirming the heterogeneity of the pH profiles within these biofilms. pH was also analyzed following glucose addition to both suspended and attached cultures. In both cases, the pH became more acidic, likely due to glucose metabolism causing the release of tricarboxylic acid cycle acids and CO(2). These studies demonstrate that the combination of 3D functional fluorescence imaging with well-designed nanoparticle sensors provides a powerful tool for in situ characterization of chemical microenvironments in complex biofilms.

##### Assuntos

Biofilmes/crescimento & desenvolvimento , Escherichia coli/crescimento & desenvolvimento , Fluorescência , Processamento de Imagem Assistida por Computador , Nanopartículas , Dióxido de Silício , Microbiologia da Água , Humanos , Concentração de Íons de Hidrogênio , Microscopia Confocal , Microscopia de Fluorescência*Environ Sci Technol ; 41(3): 936-41, 2007 Feb 01.*

**| MEDLINE**| ID: mdl-17328206

##### RESUMO

The spatial distribution of Cu was determined in Escherichia coli PHL628 biofilms using a scanning electrochemical microscope (SECM) consisting of a microelectrode in conjunction with a piezoelectric micropositioning system. Aqueous labile copper species were determined using voltametric stripping after reductive deposition of Cu for 4 min on the microelectrode at -0.7 V (vs Ag/AgCl). The position of the bulk solution-biofilm interface was determined from the change in current produced by 0.4 mM hydroxymethyl ferrocene that was added as a redox indicator. After a 2 h exposure to 0.2 mM copper, Cu was located in the upper region of the biofilm with a penetration depth less than 150 microm. A one-dimensional diffusive transport model adequately described the spatial distribution of copper in the biofilm, but the Cu retardation factor in the biofilm was more than 6-fold larger than that calculated from the isotherm for Cu binding to suspensions of E. coli PHL628 cells. There are several possible reasons for this difference, including an increase in the amount of extracellular polymer per cell within the biofilm and/or tortuosity that might hinder Cu transport into biofilms. The SECM technique in combination with model calculations provides direct evidence in support of the concept that formation of a biofilm may confer resistance to transient spikes in the bulk solution concentration of toxic metal species by retarding metal diffusion and reducing the metal exposure of cells within the biofilm.