A model accounting for finite spatial dimensions of the deposit patterns in the evaporating sessile drops of colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite volume and hence these dimensions are of the steric origin. Within this model, the geometrical characteristics of the deposition patterns are found as functions of the initial concentration of the solute, the initial geometry of the drop, and the time elapsed from the beginning of the drying process. The model is solved analytically for small initial concentrations of the solute and numerically for arbitrary initial concentrations of the solute. The agreement between our theoretical results and the experimental data is demonstrated, and it is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles. These results are universal and do not depend on any free or fitting parameters; they are important for understanding the evaporative deposition and may be useful for creating controlled deposition patterns.PACS: 47.55.Dz -Drops and bubbles; 68.03.Fg -Evaporation and condensation; 81.15.-z -Methods of deposition of films and coatings; film growth and epitaxy.
We study the elastic response of a wormlike polymer chain with reversible kinklike structural defects. This is a generic model for (a) the double-stranded DNA with sharp bends induced by binding of certain proteins, and (b) effects of trans-gauche rotations in the backbone of the single-stranded DNA. The problem is solved both analytically and numerically by generalizing the well-known analogy to the quantum rotator. In the small stretching force regime, we find that the persistence length is renormalized due to the presence of the kinks. In the opposite regime, the response to the strong stretching is determined solely by the bare persistence length with exponential corrections due to the "ideal gas of kinks." This high-force behavior changes significantly in the limit of high bending rigidity of the chain. In that case, the leading corrections to the mechanical response are likely to be due to the formation of multikink structures, such as kink pairs.
Using the complex Langevin sampling strategy, field theoretic simulations are performed to study the equilibrium phase behavior and structure of symmetric polycation-polyanion mixtures without salt in good solvents. Static structure factors for the segment density and charge density are calculated and used to study the role of fluctuations in the electrostatic and chemical potential fields beyond the random phase approximation. We specifically focus on the role of charge density and molecular weight on the structure and complexation behavior of polycation-polyanion solutions. A demixing phase transition to form a "complex coacervate" is observed in strongly charged systems, and the corresponding spinodal and binodal boundaries of the phase diagram are investigated.
This viewpoint article is intended as a brief introduction to the emerging subject of field-theoretic simulations (FTS) of charged polymers. While the direct numerical simulation of field theory models has begun to impact several traditional areas of polymer science, including blends and block copolymers, polyelectrolytes have hitherto not been the subject of field-theoretic simulations.Here we report on a preliminary FTS study of polyelectrolyte complexation that demonstrates the potential of this novel numerical approach.Polyelectrolytes are ubiquitous in nature and in applications ranging from personal care products to paints, coatings, and processed foods. Indeed, practically all biopolymers are polyelectrolytes. In the application context, the introduction of dissociable groups is one of the most powerful ways to confer water solubility on a polymeric material. Scientifically, the polymer bound charges, which are compensated by a sea of oppositely charged counterions, produce a coupling between chain conformations and electrostatics that leads to an incredible richness of polyelectrolyte phenomena. However, this richness comes with a price: charged polymers are among the most difficult polymer systems to study theoretically or to simulate on the computer [1,2,3,4]. The explanation lies in the long range nature of Coulomb interactions -charged segments feel each other at much larger distances than segments in neutral polymer systems.
Solids dispersed in a drying drop migrate to the (pinned) contact line. This migration is caused by outward flows driven by the loss of the solvent due to evaporation and by geometrical constraint that the drop maintains an equilibrium surface shape with a fixed boundary. Here, in continuation of our earlier paper, we theoretically investigate the evaporation rate, the flow field, and the rate of growth of the deposit patterns in a drop over an angular sector on a plane substrate. Asymptotic power laws near the vertex (as distance to the vertex goes to zero) are obtained. A hydrodynamic model of fluid flow near the singularity of the vertex is developed and the velocity field is obtained. The rate of the deposit growth near the contact line is found in two time regimes. The deposited mass falls off as a weak power gamma of distance close to the vertex and as a stronger power beta of distance further from the vertex. The power gamma depends only slightly on the opening angle alpha and stays roughly between -1/3 and 0. The power beta varies from -1 to 0 as the opening angle increases from 0 degrees to 180 degrees. At a given distance from the vertex, the deposited mass grows faster and faster with time, with the greatest increase in the growth rate occurring at the early stages of the drying process.
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