Faculty Bibliography

We consider the model of random sequential adsorption, with the depositing objects, as well as those already at the surface, decreasing in size according to a specified time dependence, from a larger initial value to a finite value in the large-time limit. Numerical Monte Carlo simulations of two-dimensional deposition of disks and one-dimensional deposition of segments are reported for the density-density correlation function and gap-size distribution function, respectively. Analytical considerations supplement numerical results in the one-dimensional case. We investigate the correlation hole-the depletion of correlation functions near contact and, for the present model, their vanishing at contact-that opens up at finite times, as well as its closing and reemergence of the logarithmic divergence of correlation properties at contact in the large-time limit.

We develop an approach aimed at optimizing the parameters of a network of biochemical logic gates for reduction of the "analog" noise buildup. Experiments for three coupled enzymatic AND gates are reported, illustrating our procedure. Specifically, starch, one of the controlled network inputs, is converted to maltose by beta-amylase. With the use of phosphate (another controlled input), maltose phosphorylase then produces glucose. Finally, nicotinamide adenine dinucleotide (NAD(+)), the third controlled input, is reduced under the action of glucose dehydrogenase to yield the optically detected signal. Network functioning is analyzed by varying selective inputs and fitting standardized few-parameters "response-surface" functions assumed for each gate. This allows a certain probe of the individual gate quality, but primarily yields information on the relative contribution of the gates to noise amplification. The derived information is then used to modify our experimental system to put it in a regime of a less noisy operation.

We survey our research on modeling the mechanisms of control of uniformity in the growth of nanosize and colloid size particles. The former are produced as nanocrystals by burst nucleation from solution and the latter are formed by self-assembly (aggregation) of the nanocrystals. In the colloid particle synthesis, the two dynamical processes are coupled, both governed by diffusional transport of the respective building blocks (monomers). The interrelation of the two processes allows for the synthesis of narrow size distribution colloid dispersions, which are of importance in many applications. We first review a mathematical model of diffusive cluster growth by the capture of monomer "singlets." We then analyze burst nucleation of nanoparticles in solution. Finally, we couple it to the secondary process of aggregation of nanoparticles to form colloids and discuss various aspects of the modeling of particle size distribution, as well as other features of the processes considered.

We report numerical investigations of a 3D model of diffusive growth of fine particles, the internal structure of which corresponds to different crystal lattices. A growing cluster (particle) is immersed in and exchanges monomer building blocks with a surrounding medium of diffusing (off-lattice) monomers. On-surface dynamics of the latter is accounted for by allowing, in addition to detachment, monomer motion to the neighboring vacant crystal sites, according to probabilistic rules mimicking local thermalization. The key new feature of our model is the focus on the growth of a single cluster, emerging as a crystalline core, without development of defects that can control large-scale growth modes. This single, defect-free core growth is imposed by the specific dynamic rules assumed. Our results offer a possible explanation of the experimentally observed shape uniformity (i.e., fixed, approximately evenly sized proportions) in the synthesis of uniform colloids and nanoparticles. We demonstrate the basic principles of well-defined particle shape emergence in such growth. Specifically, several shapes are possible for a given crystal structure. The formation of shapes that follow the crystal symmetry and are uniform can be a result of the nonequilibrium nature of the growth process. The shape of a growing particle can be controlled by varying the relative rates of kinetic processes as well as by adjusting the concentration of monomers in the surrounding medium.

In this work we extend recent study of the properties of the dense packing of "superdisks," by Y. Jiao [Phys. Rev. Lett. 100, 245504 (2008)] to the jammed state formed by these objects in random sequential adsorption. The superdisks are two-dimensional shapes bound by the curves of the form |x|2p+|y|2p=1, with p>0. We use Monte Carlo simulations and theoretical arguments to establish that p=1/2 is a special point at which the jamming density, rhoJ(p), has a discontinuous derivative as a function of p . The existence of this point can be also argued for by a phenomenological excluded-area argument.

Electrode-immobilized glucose-6-phosphate dehydrogenase is used to catalyze an enzymatic reaction which carries out the AND logic gate. This logic function is considered here in the context of biocatalytic processes utilized for the biocomputing applications for "digital" (threshold) sensing/actuation. We outline the response functions desirable for such applications and report the first experimental realization of a sigmoid-shape response in one of the inputs. A kinetic model is developed and utilized to evaluate the extent to which the experimentally realized gate is close to optimal.

In this work, we demonstrate both experimentally and theoretically that the analog noise generation by a single enzymatic logic gate can be dramatically reduced to yield gate operation with virtually no input noise amplification. We demonstrate that when a cosubstrate with a much smaller affinity than the primary substrate is used, a negligible increase in the noise output from the logic gate is obtained, as compared to the input noise level. Our general theoretical conclusions were confirmed by experimental realizations of the AND logic gate based on the enzyme horseradish peroxidase using hydrogen peroxide as the substrate, with 2,2'-azino-bis(3-ethylbenzthiazoline-6-sulfonic acid) or ferrocyanide as cosubstrates with vastly different rate constants.

The phenomenon of burst nucleation in solution, in which a period of apparent chemical inactivity is followed by a sudden and explosive growth of nucleated particles from a solute species, has been given a widely accepted qualitative explanation by LaMer and co-workers. Here, we present a model with the assumptions of instantaneous re-thermalization below the critical nucleus size and irreversible diffusive growth above the critical size, which for the first time formulates LaMer's explanation of burst nucleation in a manner allowing quantitative calculations. The behavior of the model at large times, t, is derived with the result that the average cluster size, as measured by the number of atoms, grows approximately t, while the width of the cluster distribution grows approximately (sq root)1. We develop an effective numerical scheme to integrate the equations of the model and compare the asymptotic expressions to results from numerical simulation. Finally, we discuss the physical effects which cause real nucleation processes in solution to deviate from the behavior of the model.

We study the effect of the presence of a regular substrate pattern on the irreversible adsorption of nanosized and colloid particles. Deposition of disks of radius r(0) is considered, with the allowed regions for their center attachment at the planar surface consisting of square cells arranged in a square lattice pattern. We study the jammed state properties of a generalized version of the random sequential adsorption model for different values of the cell size, a , and cell-cell separation, b . The model shows a surprisingly rich behavior in the space of the two dimensionless parameters alpha = a / 2r(0) and beta = b / 2r(0) . Extensive Monte Carlo simulations for system sizes of 500 x 500 square lattice unit cells were performed by utilizing an efficient algorithm, to characterize the jammed state morphology.