Random sequential adsorption of lines and ellipses

Changes in Secondary Structure and Properties of Bovine Serum Albumin as a Result of Interactions with Gold Surface

Proteins can alter their shape when interacting with a surface. This study explores how bovine serum albumin (BSA) modifies structurally when it adheres to a gold surface, depending on the protein concentration and pH. We verified that the gold surface induces significant structural modifications to the BSA molecule using circular dichroism, infrared spectroscopy, and atomic force microscopy. Specifically, adsorbed molecules displayed increased levels of disordered structures and β-turns, with fewer α-helices than the native structure. MP-SPR spectroscopy demonstrated that the protein molecules preferred a planar orientation during adsorption. Molecular dynamics simulations revealed that the interaction between cysteines exposed to the outside of the molecule and the gold surface was vital, especially at pH=3.5. The macroscopic properties of the protein film observed by AFM and contact angles confirm the flexible nature of the protein itself. Notably, structural transformation is joined with the degree of hydration of protein layers.

Two-stage random sequential adsorption of discorectangles and disks on a two-dimensional surface

The different variants of two-stage random sequential adsorption (RSA) models for packing of disks and discorectangles on a two-dimensional (2D) surface were investigated. In the SD (sticks+disks) model, the discorectangles were first deposited and then the disks were added. In the DS (disks+sticks) model, the disks were first deposited and then discorectangles were added. At the first stage the particles were deposited up to the selected concentration and at the final (second) stage the particles were deposited up to the saturated (jamming) state. The main parameters of the models were the concentration of particles deposited at the first stage, aspect ratio of the discorectangles ɛ (length to diameter of ratio ɛ=l/d) and disk diameter D. All distances were measured using the value of d as a unit of measurement of linear dimensions, the disk diameter was varied in the interval D∈[1-10], and the aspect ratio value was varied in the interval ɛ∈[1-50]. The dependencies of the jamming coverage of particles deposited at the second stage versus the parameters of the models were analyzed. The presence of first deposited particles for both models regulated the maximum possible disk diameter D_{max} (SD model) or the maximum aspect ratio ɛ_{max} (DS model). This behavior was explained by the deposition of particles in the second stage into triangular (SD model) or elongated (DS model) pores formed by particles deposited at the first stage. The percolation connectivity of disks (SD model) and discorectangles (DS model) for the particles with a hard core and a soft shell structure was analyzed. The disconnectedness was ensured by overlapping of soft shells. The dependencies of connectivity versus the parameters of SD and DS models were also analyzed.

Structure of saturated random-sequential-adsorption ellipse packings

Motivated by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of (asymptotically) saturated RSA ellipse packings. We determine the packing fractions ϕ_{s}(α) to high precision, finding an empirical analytic formula that predicts ϕ_{s}(α) to within less than 0.1% for all α≤10. Then we explore how these packings' positional-orientational order varies with α. We find a transition from tip/side- to side/side-contact-dominated structure at α=α_{TS}≃2.4. At this aspect ratio, the peak value g_{max} of packings' positional-orientational pair correlation functions is minimal, and systems can be considered maximally locally disordered. For smaller (larger) α, g_{max} increases exponentially with deceasing (increasing) α. Local nematic order and structures comparable to the precursor domains observed in experiments gradually emerge as α increases beyond three. For α≳5, single-layer lamellae become more prominent and long-wavelength density fluctuations increase with α as packings gradually approach the rodlike limit.

Confinement effects on the random sequential adsorption packings of elongated particles in a slit

The behavior of a system of two-dimensional elongated particles (discorectangles) packed in a slit between the two parallel walls was analyzed using a simulation approach. The packings were produced using the random sequential adsorption model with continuous positional and orientational degrees of freedom. The aspect ratio (length-to-width ratio, ɛ=l/d) of the particles was varied within the range ɛ∈[1;32] while the distance between the walls was varied within the range h/d∈[1;80]. The properties of deposits in jammed state [the coverage, the order parameter, and the long-range (percolation) connectivity between particles] were studied numerically. The values of ɛ and h significantly affected the structure of the packings and the percolation connectivity. Particularly, the observed nontrivial dependencies of the jamming coverage φ(ɛ) or φ(h) were explained by the interplay of the different geometrical factors related to confinement, particle orientation degrees of freedom and excluded volume effects.

Connectedness percolation in the random sequential adsorption packings of elongated particles

Connectedness percolation phenomena in the two-dimensional packing of elongated particles (discorectangles) were studied numerically. The packings were produced using random sequential adsorption off-lattice models with preferential orientations of the particles along a given direction. The partial ordering was characterized by the order parameter S, with S=0 for completely disordered films (random orientation of particles) and S=1 for completely aligned particles along the horizontal direction x. The aspect ratio (length-to-width ratio) of the particles was varied within the range ɛ∈[1;100]. Analysis of connectivity was performed assuming a core-shell structure of the particles. The value of S affected the structure of the packings, the formation of long-range connectivity, and the behavior of the electrical conductivity. The effects can be explained by taking accounting of the competition between the particles' orientational degrees of freedom and excluded volume effects. For aligned deposition, anisotropy in the electrical conductivity was observed with the values along the alignment direction σ_{x} being larger than the values in the perpendicular direction σ_{y}. Anisotropy in the localization of the percolation threshold was also observed in finite-sized packings, but it disappeared in the limit of infinitely large systems.

Characterization of domain formation during random sequential adsorption of stiff linear k-mers onto a square lattice

Using a computer simulation, we have studied the random sequential adsorption of stiff linear k-mers onto a square lattice. Each such particle occupies k adjacent lattice sites. During deposition, the two mutually perpendicular orientations of the particles are equiprobable, hence, a macroscopically isotropic monolayer is formed. However, this monolayer is locally anisotropic, since the deposited particles tend to form domains of particles with the same orientation. Using the "excluded area" concept, we have classified lattice sites into several types and examined how the fraction of each type of lattice site varies as the number of deposited particles increases. The behaviors of these quantities have allowed us to identify the following stages of domain formation: (i) the emergence of domain seeds, (ii) the filling of domains, and (iii) densification of the domains.

Random sequential adsorption of partially ordered discorectangles onto a continuous plane

A computer simulation was used to study the random sequential adsorption of identical discorectangles onto a continuous plane. The problem was analyzed for a wide range of discorectangle aspect ratios (ɛ∈[1;100]). We studied the anisotropic deposition, i.e., the orientations of the deposited particles were uniformly distributed within some interval such that the particles were preferentially aligned along a given direction. The kinetics of the changes in the packing fraction found at different values of such the alignment are discussed. Partial ordering of the discorectangles significantly affected the packing fraction at the jamming state, φ_{j}, and shifted the cusps in the φ_{j}(ɛ) dependencies. The structure of the jammed state was analyzed using the adsorption of disks of different diameters into the porous space between the deposited discorectangles. The analysis of the connectivity between the discorectangles was performed assuming a core-shell structure of particles.

Mechanism of lysozyme adsorption onto gold surface determined by quartz crystal microbalance and surface plasmon resonance

In this study, the physicochemical characterization of lysozyme adsorbed on gold was investigated. Through the use of MP-SPR it was possible to establish that the orientation of molecules changes from side-on to between or end-on with increasing surface coverage. The data confirms that the process of adsorption is driven primarily by electrostatic interactions but also by hydrophobic forces. MP-SPR data was compared with the Random Sequential Adsorption model for a molecule with an ellipsoidal shape. Contact angle measurements showed that higher surface coverage also translates in more hydrophilic properties of obtained lysozyme layer. Comparison of CD and PM-IRRAS spectra in solution and adsorbed state respectively showed changes in the secondary structures of lysozyme. These changes are dependent on pH, but fundamentally they go in the direction of the increase of β-turn/random content with a simultaneous decrease in β-sheet fraction, which suggests that aggregation is not occurring. The combination of MP-SPR and QCM-D measurements allowed the estimation of the number of water molecules associated with the lysozymes films. It has been observed that hydration decreases from 70% in pH = 4 to 30% in pH = 11. This data indicates that hydration is driven mainly by the degree of protonation of lysozyme molecules.

Random sequential adsorption of lattice animals on a three-dimensional cubic lattice

The properties of the random sequential adsorption of objects of various shapes on simple three-dimensional (3D) cubic lattice are studied numerically by means of Monte Carlo simulations. Depositing objects are "lattice animals," made of a certain number of nearest-neighbor sites on a lattice. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density θ_{J} and on the temporal evolution of the coverage fraction θ(t). We analyzed all lattice animals of size n=1, 2, 3, 4, and 5. A significant number of objects of size n⩾6 were also used to confirm our findings. Approach of the coverage θ(t) to the jamming limit θ_{J} is found to be exponential, θ_{J}-θ(t)∼exp(-t/σ), for all lattice animals. It was shown that the relaxation time σ increases with the number of different orientations m that lattice animals can take when placed on a cubic lattice. Orientations of the lattice animal deposited in two randomly chosen places on the lattice are different if one of them cannot be translated into the other. Our simulations performed for large collections of 3D objects confirmed that σ≅m∈{1,3,4,6,8,12,24}. The presented results suggest that there is no correlation between the number of possible orientations m of the object and the corresponding values of the jamming density θ_{J}. It was found that for sufficiently large objects, changing of the shape has considerably more influence on the jamming density than increasing of the object size.

Random sequential adsorption on Euclidean, fractal, and random lattices

Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal, and random lattices is studied. The adsorption process is modeled by using random sequential adsorption algorithm. Objects are adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski carpets having dimension d between 1 and 2, and on Erdős-Rényi random graphs. The number of sites is M=L^{d} for Euclidean and fractal lattices, where L is a characteristic length of the system. In the case of random graphs, such a characteristic length does not exist, and the substrate can be characterized by a fixed set of M vertices (sites) and an average connectivity (or degree) g. This paper concentrates on measuring (i) the probability W_{L(M)}(θ) that a lattice composed of L^{d}(M) elements reaches a coverage θ and (ii) the exponent ν_{j} characterizing the so-called jamming transition. The results obtained for Euclidean, fractal, and random lattices indicate that the quantities derived from the jamming probability W_{L(M)}(θ), such as (dW_{L}/dθ)_{max} and the inverse of the standard deviation Δ_{L}, behave asymptotically as M^{1/2}. In the case of Euclidean and fractal lattices, where L and d can be defined, the asymptotic behavior can be written as M^{1/2}=L^{d/2}=L^{1/ν_{j}}, with ν_{j}=2/d.

Induction of transferrin aggregation by indazolium [tetrachlorobis(1H-indazole)ruthenate(iii)] (KP1019) and its biological function

Pre-incubation ofKP1019with transferrin leads to the formation of adducts/aggregates, which inhibit the cytotoxic properties ofKP1019.

Random sequential adsorption of cuboids

The subject of this study was random sequential adsorption of cuboids of axes length ratio of a : 1 : b for a ∈ [0.3, 1.0] and b ∈ [1.0, 2.0], and the aim of this study was to find a shape that provides the highest packing fraction. The obtained results show that the densest packing fraction is 0.401 87 ± 0.000 97 and is reached for axes ratios near cuboids of 0.75:1:1.30. Kinetics of packing growth was also studied, and it was observed that its power-law character seems not to be governed by the number of cuboid degrees of freedom. The microstructural properties of obtained packings were studied in terms of density correlation function and propagation of orientational ordering.

Anisotropy in electrical conductivity of two-dimensional films containing aligned nonintersecting rodlike particles: Continuous and lattice models

The electrical conductivity of two-dimensional films filled with rodlike particles (rods) was simulated by the Monte Carlo method. The main attention has been paid to the investigation of the effect of the rod alignment on the electrical properties of the films. Both continuous and lattice approaches were used. Intersections of particles were forbidden. Our main findings are (i) both models demonstrate similar behaviors, (ii) at low concentration of rods, both approaches lead to the same dependencies of the electrical conductivity on the concentration of the rods, (iii) the alignment of the rods essentially affects the electrical conductivity, (iv) at some concentrations of partially aligned rods, the films may be conducting only in one direction, and (v) the films may simultaneously be both highly transparent and electrically anisotropic.

Precise algorithm to generate random sequential adsorption of hard polygons at saturation

Random sequential adsorption (RSA) is a time-dependent packing process, in which particles of certain shapes are randomly and sequentially placed into an empty space without overlap. In the infinite-time limit, the density approaches a "saturation" limit. Although this limit has attracted particular research interest, the majority of past studies could only probe this limit by extrapolation. We have previously found an algorithm to reach this limit using finite computational time for spherical particles and could thus determine the saturation density of spheres with high accuracy. In this paper, we generalize this algorithm to generate saturated RSA packings of two-dimensional polygons. We also calculate the saturation density for regular polygons of three to ten sides and obtain results that are consistent with previous, extrapolation-based studies.

Vertical drying of a suspension of sticks: Monte Carlo simulation for continuous two-dimensional problem

The vertical drying of a two-dimensional colloidal film containing zero-thickness sticks (lines) was studied by means of kinetic Monte Carlo (MC) simulations. The continuous two-dimensional problem for both the positions and orientations was considered. The initial state before drying was produced using a model of random sequential adsorption with isotropic orientations of the sticks. During the evaporation, an upper interface falls with a linear velocity in the vertical direction, and the sticks undergo translational and rotational Brownian motions. The MC simulations were run at different initial number concentrations (the numbers of sticks per unit area), p_{i}, and solvent evaporation rates, u. For completely dried films, the spatial distributions of the sticks, the order parameters, and the electrical conductivities of the films in both the horizontal, x, and vertical, y, directions were examined. Significant evaporation-driven self-assembly and stratification of the sticks in the vertical direction was observed. The extent of stratification increased with increasing values of u. The anisotropy of the electrical conductivity of the film can be finely regulated by changes in the values of p_{i} and u.

Adsorption effectiveness of β-lactoglobulin onto gold surface determined by quartz crystal microbalance

Bovine β-lactoglobulin (LGB) is a transport protein that can bind to its structure hydrophobic bioactive molecules. Due to the lack of toxicity, high stability and pH-dependent molecular binding mechanism, lactoglobulin can be used as a carrier of sparingly soluble drugs. Dynamic light scattering has confirmed LGB's tendency to create oligomeric forms. The hydrodynamic diameter of LGB molecules varies from 4 nm to 6 nm in the pH range of 2-10 and ionic strength I = 0.001-0.15 M, which corresponds to the presence of mono or dimeric LGB forms. The LGB zeta potential varies from 26.5 mV to -33.3 mV for I = 0.01 M and from 13.3 mV to -16 mV for I = 0.15 M in the pH range of 2-10. The isoelectric point is at pH 4.8. As a result of strong surface charge compensation, the maximum effective ionization degree of the LGB molecule is 35% for ionic strength I = 0.01 M and 22% for I = 0.15 M. The effectiveness of adsorption is linked with the properties of the protein, as well as those of the adsorption surface. The functionalization of gold surfaces with β-lactoglobulin (LGB) was studied using a quartz crystal microbalance with energy dissipation monitoring (QCM-D). The effectiveness of LGB adsorption correlates strongly with a charge of gold surface and the zeta potential of the molecule. The greatest value of the adsorbed mass was observed in the pH range in which LGB has a positive zeta potential values, below pH 4.8. This observation shows that electrostatic interactions play a dominant role in LGB adsorption on gold surfaces. Based on the adsorbed mass, protein orientation on gold surfaces was determined. The preferential side-on orientation of LGB molecules observed in the adsorption layer is consistent with the direction of the molecule dipole momentum determined by molecular dynamics simulations of the protein (MD). The use of the QCM-D method also allowed us to determine the effectiveness of adsorption of LGB on gold surface. Knowing the mechanism of LGB adsorption is significant importance for determining the optimum conditions for immobilizing this protein on solid surfaces. As β-lactoglobulin is a protein that binds various ligands, the binding properties of immobilized β-lactoglobulin can be used to design controlled protein structures for biomedical applications.

Shape Universality Classes in the Random Sequential Adsorption of Nonspherical Particles

Random sequential adsorption (RSA) of particles of a particular shape is used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the observed algebraic time dependence of the asymptotic jamming coverage ∼t^{-ν} as t→∞. However, the exact value of the exponent ν is not known apart from the simplest case of the RSA of monodisperse spheres adsorbed on a line (Renyi's seminal "car parking problem"), where ν=1 can be derived analytically. Empirical simulation studies have conjectured on a case-by-case basis that for general nonspherical particles, ν=1/(d+d[over ˜]), where d denotes the dimension of the domain, and d[over ˜] the number of orientational degrees of freedom of a particle. Here, we solve this long-standing problem analytically for the d=1 case-the "Paris car parking problem." We prove, in particular, that the scaling exponent depends on the particle shape, contrary to the original conjecture and, remarkably, falls into two universality classes: (i) ν=1/(1+d[over ˜]/2) for shapes with a smooth contact distance, e.g., ellipsoids, and (ii) ν=1/(1+d[over ˜]) for shapes with a singular contact distance, e.g., spherocylinders and polyhedra. The exact solution explains, in particular, why many empirically observed scalings fall in between these two limits.

Particle morphology effects in random sequential adsorption

The properties of the random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps, whereby the size of the objects is gradually increased by wrapping the walks in several different ways. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density θ_{J} and on the temporal evolution of the coverage fraction θ(t). Our results suggest that the order of symmetry axis of a shape exerts a decisive influence on adsorption kinetics near the jamming limit θ_{J}. The decay of probability for the insertion of a new particle onto a lattice is described in a broad range of the coverage θ by the product between the linear and the stretched exponential function for all examined objects. The corresponding fitting parameters are discussed within the context of the shape descriptors, such as rotational symmetry and the shape factor (parameter of nonsphericity) of the objects. Predictions following from our calculations suggest that the proposed fitting function for the insertion probability is consistent with the exponential approach of the coverage fraction θ(t) to the jamming limit θ_{J}.

Shapes for maximal coverage for two-dimensional random sequential adsorption

Maximal possible saturated random packing fractions and corresponding values of anisotropy level for which they are reached.

Precise algorithm to generate random sequential addition of hard hyperspheres at saturation

The study of the packing of hard hyperspheres in d-dimensional Euclidean space R^{d} has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. E 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g(2)(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed "decorrelation" principle, and the degree of "hyperuniformity" (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average Voronoi cell. Our algorithm is easily generalizable to generate saturated RSA packings of nonspherical particles.

Simulation study of anisotropic random sequential adsorption of extended objects on a triangular lattice

The properties of the anisotropic random sequential adsorption (RSA) of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps, whereby the first step determines the orientation of the object. Anisotropy is introduced by positing unequal probabilities for orientation of depositing objects along different directions of the lattice. This probability is equal p or (1-p)/2, depending on whether the randomly chosen orientation is horizontal or not, respectively. Approach of the coverage θ(t) to the jamming limit θ(jam) is found to be exponential θ(jam)-θ(t)is proportional to exp(-t/σ), for all probabilities p. It was shown that the relaxation time σ increases with the degree of anisotropy in the case of elongated and asymmetrical shapes. However, for rounded and symmetrical shapes, values of σ and θ(jam) are not affected by the presence of anisotropy. We finally analyze the properties of the anisotropic RSA of polydisperse mixtures of k-mers. Strong dependencies of the parameter σ and the jamming coverage θ(jam) on the degree of anisotropy are obtained. It is found that anisotropic constraints lead to the increased contribution of the longer k-mers in the total coverage fraction of the mixture.

Random sequential adsorption of polyatomic species on fractal substrates

Random sequential adsorption of k-mers of different sizes and shapes deposited on two types of fractal surfaces (deterministic and statistical) is studied. These kinds of substrates present intrinsic heterogeneities. As a consequence, the average coordination number depends on the topology that characterizes the adsorbent. For discrete models, at the late stage the surface coverage evolves according to θ(t)=θ(j)-Aexp[-t/σ], where θ(j) is the jamming coverage while A and σ are fitting parameters. A detailed analysis of how these main quantities [θ(j), σ] depend on the relationship between the geometry of the adsorbate and the adsorbent is presented. The results obtained suggest that the symmetry of the substrate may exert a decisive influence on the adsorption kinetics of polyatomic species.

Universality of the power-law approach to the jamming limit in random sequential adsorption dynamics

Random sequential adsorption (RSA), on a two-dimensional continuum substrate, of different types of zero area objects that disallow domain formation and hence lead to jamming, is examined by simulation. In all the cases, in the asymptotic time regime, the approach of the number density rho(t) at instant t to jamming density rho(infinity) is found to exhibit power law rho(infinity)-rho(t) approximately t{-p} as that for RSA of finite area objects. These results suggest the possibility of the power law being universal for all jamming systems in RSA on a continuum substrate. A generalized analytical treatment is also proposed.

Percolation of polyatomic species with the presence of impurities

In this paper, the percolation of (a) linear segments of size k and (b) k-mers of different structures and forms deposited on a square lattice contaminated with previously adsorbed impurities have been studied. The contaminated or diluted lattice is built by randomly selecting a fraction of the elements of the lattice (either bonds or sites) which are considered forbidden for deposition. Results are obtained by extensive use of finite size scaling theory. Thus, in order to test the universality of the phase transition occurring in the system, the numerical values of the critical exponents were determined. The characteristic parameters of the percolation problem are dependent not only on the form and structure of the k-mers but also on the properties of the lattice where they are deposited. A phase diagram separating a percolating from a nonpercolating region is determined as a function of the parameters of the problem. A comparison between random site and random bond percolation in the presence of impurities on the lattice is presented.

The effect of impurities on jamming in random sequential adsorption of elongated objects

We consider the jamming aspect of random sequential adsorption of extended particles onto two-dimensional lattice by computer Monte Carlo simulations. The initial presence of impurities on the substrate disturbs this phenomenon significantly and we study here how the size and density of impurity particles affect the resulting jamming threshold. We present the formula for jamming threshold as a closed function of all important parameters (the size of primary particles, the size of impurity particles, and the final density of impurities). The fractal dimension of the space free of impurities is also discussed.

Site-bond percolation of polyatomic species

A generalization of the classical monomer site-bond percolation problem is studied in which linear k-uples of nearest neighbor sites (site k-mers) and linear k-uples of nearest neighbor bonds (bond k-mers) are independently occupied at random on a square lattice. We called this model the site-bond percolation of polyatomic species or k-mer site-bond percolation. Motivated by considerations of cluster connectivity, we have used two distinct schemes (denoted as S intersection of B and S union of B) for k-mer site-bond percolation. In S intersection of B(S union of B), two points are said to be connected if a sequence of occupied sites and (or) bonds joins them. By using Monte Carlo simulations and finite-size scaling theory, data from S intersection of B and S union of B are analyzed in order to determine the critical curves separating the percolating and nonpercolating regions.

Shape effects in random sequential adsorption of zero-area angled objects on a continuum substrate

Random sequential adsorption (RSA) of zero-area symmetric angled objects on a continuum substrate is studied for the full range (0 degrees -180 degrees ) of values of the arm angle straight phi. The value of exponent alpha [in rho(t) approximately t(alpha), where rho(t) is the number density] exhibits a dramatic crossover feature near straight phi = 0 degrees or 180 degrees. It is shown that the functional dependence of alpha on straight phi is governed by the degree of shape dependent frustration of the adsorption process. The crucial role of the geometrical character of the zero-area object in RSA dynamics is thus established.