Rough growth and morphological instability of compact electrodeposits

Nonuniversality of front fluctuations for compact colonies of nonmotile bacteria

The front of a compact bacterial colony growing on a Petri dish is a paradigmatic instance of non-equilibrium fluctuations in the celebrated Eden, or Kardar-Parisi-Zhang (KPZ), universality class. While in many experiments the scaling exponents crucially differ from the expected KPZ values, the source of this disagreement has remained poorly understood. We have performed growth experiments with B. subtilis 168 and E. coli ATCC 25922 under conditions leading to compact colonies in the classically alleged Eden regime, where individual motility is suppressed. Non-KPZ scaling is indeed observed for all accessible times, KPZ asymptotics being ruled out for our experiments due to the monotonic increase of front branching with time. Simulations of an effective model suggest the occurrence of transient nonuniversal scaling due to diffusive morphological instabilities, agreeing with expectations from detailed models of the relevant biological reaction-diffusion processes.

Crossover from compact to branched films in electrodeposition with surface diffusion

We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of G hop attempts (G≫1), a detachment probability ε<1 per neighboring particle, and a no-desorption condition. Computer simulations show the formation of a compact wetting layer followed by the growth of branched deposits. The maximal thickness z_{c} of that layer increases with G but is weakly affected by ε. A scaling approach describes the crossover from smooth film growth to unstable growth and predicts z_{c}∼G^{γ}, with γ=1/[2(1-ν)]≈0.43, where ν≈0.30 is the inverse of the dynamical exponent of the Villain-Lai-Das Sarma equation that describes the initial roughening. Using previous results for related deposition models, the thickness z_{c} can be predicted as a function of an activation energy for terrace surface diffusion and the temperature, and the small effects of the parameter ε are justified. These predictions are confirmed by the numerical results with good accuracy. We discuss possible applications, with a particular focus on the growth of multifuncional structures with stacking layers of different porosity.

Anomalous roughening of curvature-driven growth with a variable interface window

We studied the curvature-driven roughening of a disk domain pattern with a variable interface window. The relaxation of interface is driven by negative "surface tension." When a domain boundary propagates radially at a constant rate, we found that evolution of interface roughness follows scaling dynamic behavior. The local growth exponents are substantially different from the global exponents. Curvature-driven roughening belongs to a new class of anomalous roughening dynamics. However, a different "surface tension" leads to different global exponents. This is different from that of interface evolution with a fixed-size window, which has universal exponent. The variable growth window leads to a class of anomalous roughening dynamics.

State selection in the noisy stabilized Kuramoto-Sivashinsky equation

In this work, we study the one-dimensional stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states. Some connections to the phenomenon of state selection in driven out of equilibrium systems are made.

Unified moving-boundary model with fluctuations for unstable diffusive growth

We study a moving-boundary model of nonconserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin-film production by chemical vapor deposition and electrochemical deposition. The model also incorporates noise terms that account for fluctuations in the diffusive and attachment processes. A small-slope approximation allows us to derive effective interface evolution equations (IEEs) in which parameters are related to those of the full moving-boundary problem. In particular, the form of the linear dispersion relation of the IEE changes drastically for slow or for instantaneous attachment kinetics. In the former case the IEE takes the form of the well-known (noisy) Kuramoto-Sivashinsky equation, showing a morphological instability at short times that evolves into kinetic roughening of the Kardar-Parisi-Zhang (KPZ) class. In the instantaneous kinetics limit, the IEE combines the Mullins-Sekerka linear dispersion relation with a KPZ nonlinearity, and we provide a numerical study of the ensuing dynamics. In all cases, the long preasymptotic transients can account for the experimental difficulties in observing KPZ scaling. We also compare our results with relevant data from experiments and discrete models.

Microscopic model of diffusion limited aggregation and electrodeposition in the presence of leveling molecules

We present a cellular automata approach for microscopic modeling of the effect of unbinding in diffusion limited aggregation. The automata represent active particles, which are able to change their internal state and affect their neighbors. The geometry resembles electrochemical deposition-"ions" diffuse at random from the top of a container until encountering an aggregate in contact with the bottom, to which they stick. This model exhibits dendritic (fractal) growth in the diffusion limited case. The addition of a field eliminates the fractal nature but the density remains low. The addition of molecules that unbind atoms from the aggregate transforms the deposit to a 100% dense one (in three dimensions). The molecules are remarkably adept at avoiding being trapped. This mimics the effect of so-called leveler molecules which are used in electrochemical deposition.

Morphological instability and additive-induced stabilization in electrodeposition

Experiments show that electrodeposited (ED) films exhibit rough surfaces unless the electrochemical bath contains small quantities of molecular "additive" species. We develop a model for ED with additives which shows the suppression of the morphological instability by preferential additive accumulation near surface protrusions due to complex formation and additive codeposition, and subsequent growth site blocking. Linearly stable growth can be achieved over a wide range of deposition flux at sufficiently large additive bulk concentration. We predict the growth conditions necessary for level surfaces, in good agreement with experiments.

Transients due to instabilities hinder Kardar-Parisi-Zhang scaling: a unified derivation for surface growth by electrochemical and chemical vapor deposition

We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the interface equation of motion as functions of phenomenological parameters. The equation features the Kardar-Parisi-Zhang (KPZ) nonlinearity and instabilities which, depending on surface kinetics, can hinder the asymptotic KPZ scaling. Our results account for the universality and the experimental scarcity of KPZ scaling in the growth processes considered.

Multiparticle biased diffusion-limited aggregation with surface diffusion: A comprehensive model of electrodeposition

We present a complete study of the multiparticle biased diffusion-limited aggregation (MBDLA) model supplemented with surface diffusion (SD), focusing on the relevance and effects of the latter transport mechanism. By comparing different algorithms, we show that MBDLA + SD is a very good qualitative model for electrodeposition in essentially the whole range of current intensities provided one introduces SD in the model in the proper fashion. We have found that the correct procedure involves simultaneous bulk diffusion and SD, introducing a time scale arising from the ratio of the rates of the two processes. We discuss in detail the different morphologies obtained and compare them to the available experimental data with very satisfactory results. We also characterize the aggregates thus obtained by means of the dynamic scaling exponents of the interface height, allowing us to distinguish several regimes in the mentioned interface growth. Our asymptotic scaling exponents are again in good agreement with recent experiments. We conclude by discussing a global picture of the influence and consequences of SD in electrodeposition.