Laplace barriers for electrowetting thresholding and virtual fluid confinement

Reported are Laplace barriers consisting of arrayed posts or ridges that impart ～100 to 1000 s of N/m(2) Laplace pressure for fluid confinement, but the Laplace pressure is also small enough such that the barriers are porous to electrowetting control. As a result, the barriers are able to provide electrowetting flow thresholding and virtual fluid confinement in noncircular fluid geometries. A simple theoretical model for the barriers and experimental demonstrations validate functionality that may be useful for lab-on-chip, display devices, and passive matrix control, to name a few applications.     

Monte Carlo Calculations of Polymer Adsorption at the Entrance of Cylindrical Pores in Flat Adsorbing Surfaces

The influence of surface interactions on the conformation of flexible polymers partially confined inside narrow cylindrical pores in a flat surface is studied above the critical adsorption energy in a good solvent. We use a static configurational bias computational sampling method to calculate the adsorption free energy and the radius of gyration components parallel and perpendicular to the pore axis as a function of the polymer center of mass position at different degrees of confinement. We find strong free‐energy minima just in front of the pore entry for all degrees of confinement studied. At the location of the free‐energy minimum, polymers are partially adsorbed inside the pore and on the outer solid surface and adopt “drawing pin”‐like conformations. A distinct maximum in the average loop length at the pore entry indicates that the polymer bridges the pore entry of small pores.     

Interplay of symmetries of block polymers and confining geometries

The morphologies that block polymers exhibit under various types of confinement are reviewed with emphasis on experimental results and theoretical predictions. Confining geometries in all three dimensions are considered and special attention is paid to cylindrical and spherical boundary conditions. Past experimental techniques and theoretical understanding are discussed and an outlook for future advances due to the possibility for novel, well ordered and aligned morphologies to occur when polymers are confined between surfaces of varying distance, curvature, and surface chemistry is provided. Confinement creates new morphologies which are not present in the bulk, indicating that the confined thermodynamic boundary conditions result in phase behavior that is distinct from the bulk and that there is the possibility for new phases and order-order transitions to be discovered as future researchers impose new types of confinement and explore a greater range of block polymer architecture, composition and molecular weights. The article concludes with a brief introduction of interference lithography, which can be used to form arbitrary and novel boundary conditions, and a perspective on the future outlook of the phase behavior of confined block polymers.     

Partial-post Laplace barriers for virtual confinement, stable displacement, and >5 cm s(-1) electrowetting transport

Laplace barriers composed of full-posts or ridges have been previously reported as a mechanism for virtual fluid confinement, but with unstable displacement (capillary fingering or fluid trapping, respectively). A new platform of 'partial-posts' eliminates the disadvantages of full-posts or ridges, while providing ~60-80% open channel area for rapid electrowetting fluid transport (>5 cm s(-1)). The fluid mechanics of partial-post Laplace barriers are far more complex than previous Laplace barriers as it involves two mechanisms: fluid can first begin to propagate either between, or under, the partial-posts. Careful design of channel and partial-post geometries is required, else one mechanism will dominate over the other. The physics and performance of partial-post Laplace barriers are verified using theoretical equations, experimental results, and dynamic numerical modeling.     

Mo studies of polymers. I. Use of MNDO to calculate geometries,vibrational frequencies and the electronic band structures of polymers; formalism and application to polyethylene

A general treatment of linear polymers is developed using MNDO and the tight binding approximation. Analytical expressions are derived for first derivatives of the energy. These are used to calculate geometries vibration frequencies and elastic moduli. Application of this treatment to polyethylene gave results in good agreement with experiment and also a reasonable account of its electronic band structure.     

Wetting of structured hydrophobic surfaces by water droplets

Super-hydrophobic surfaces may arise due to an interplay between the intrinsic, relatively high, contact angle of the more or less hydrophobic solid surface employed and the geometric features of the solid surface. In the present work, this relationship was investigated for a range of different surface geometries, making use of surface free energy minimization. As a rule, the free energy minima (and maxima) occur when the Laplace and Young conditions are simultaneously fulfilled. Special effort has been devoted to investigating the free energy barriers present between the Cassie-Baxter (heterogeneous wetting) and Wenzel (homogeneous wetting) modes. The predictions made on the basis of the model calculations compare favorably with experimental results presented in the literature.     

APplication of Continuous Thermodynamics to the Stability of Polymer Systems. II

A determinant criterion for the critical state in solutions and mixtures of polydisperse polymers is established within the general framework of Gibbs theory. The treatment continues an earlier paper by considering more general Gibbs free energy relations: The function replacing the x-term in the classic Flory-Huggins equation is permitted to depend on a finite number of moments of the polymer distribution(s) so as to embrace most Gibbs free energy relations of practical use. The new criterion leads to a very large reduction of computer time and of needed storage capacity compared to the traditional Gibbs determinant criterion. Some relations known from the literature are shown to be special cases of the established new criterion.     

Statistical mechanical model for diffusion of simple penetrants in polymers. III. Applications—vinyl and related polymers

The theory developed in Part I of this series is modified to accommodate polymers that possess closely spaced, bulky side groups on the chains. The side groups give rise to free space between the chain “cores,” which reduces the chain separation required for penetrant motion transverse to the local chain axis. The theory is then identical to that of Part I, except that penetrant diameters minus a constant factor are employed in place of the normal diameters. In most of the cases studied the reduction factor for a given polymer may be estimated with reasonable precision from chain geometry data. This diameter-reduction effect is the likely explanation of the apparent proportionality between the activation energy of diffusion and the square of the penetrant diameter reported earlier for vinyl polymers. The data quoted here and in Part II are analyzed to give a semitheoretical correlation between the effective jump length L? and ΔE, the activation energy of diffusion. This correlation appears to be equally valid for glassy and rubbery noncrystalline polymers.     

Effects of confinement on the order-disorder transition of diblock copolymer melts

The effects of confinement on the order-disorder transition of diblock copolymer melts are studied theoretically. Confinements are realized by restricting diblock copolymers in finite spaces with different geometries (slabs, cylinders, and spheres). Within the random phase approximation, the correlation functions are calculated using the eigenvalues and eigenfunctions of the Laplacian operator inverted Delta(2) in the appropriate geometries. This leads to a size-dependent scattering function, and the minimum of the inverse scattering function determines the spinodal point of the homogeneous phase. For diblock copolymers confined in a slab or in a cylindrical nanopore, the spinodal point of the homogeneous phase (chiN)(s) is found to be independent of the confinement. On the other hand, for diblock copolymers confined in a spherical nanopore, (chiN)(s) depends on the confinement and it oscillates as a function of the radius of the sphere. Further understanding of the finite-size effects is provided by examining the fluctuation modes using the Landau-Brazovskii model.     

Confined glassy properties of polymer nanoparticles

For nearly the past two decades, significant effort has been devoted to pursuing an understanding of the glass transition temperature and associated dynamics of polymers confined to the nanoscale. Without question, we know more about the glassy properties of confined polymers today than we knew two decades ago or even a decade ago. Much of our understanding has been obtained via studies on thin polymer films, as they are facile to process and are of substantial technological importance. Nevertheless, studies on polymers confined to other geometries are becoming increasingly more important as we pursue questions difficult to address using thin films and as technology demands the use of confined polymers beyond thin films. In this feature article, we highlight the impact of nanoscale confinement on the glassy properties of polymer nanoparticles. Although the emphasis is placed on contributions from our work, a discussion of the related literature is also presented. Our aim is to elucidate commonalities or fundamental differences in the deviations of glassy properties from the bulk for polymers confined to different geometries. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

Generalized theory of capillarity for axisymmetric menisci

A high-curvature generalization of the Laplace equation of capillarity and the Young equation of capillarity (including line tension) is developed for an axisymmetric solid-liquid-fluid system. The most general expressions for the Laplace and Young equations do not assume a particular form for the specific surface free energy. However, when a particular form, i.e., ω^(A) = γ^(A)_∞+ C_JJ+ C_kK, which is related to Gibbs' expression for a highly curved menisci,¹ is assumed to hold for the specific surface free energy then we are able to recover the expected simplified form of the Laplace equation. The corresponding high-curvature Young equation includes a couple which balances the surface moments at the contact line. Unfortunately, the effect of this couple could be confused with the effect of line tension in experiments which attempt to measure the dependence of the contact angle on the contact line radius.     

Energy-driven asymmetric partitioning of a semiflexible polymer between interconnected cavities

The distribution of a semiflexible chain in the volume of two interconnected spherical cavities of equal size has been investigated by using Monte Carlo simulations. The chain possessed an extension exceeding that of the cavity, leading to large probabilities of translocated states despite the entropic penalty of passing the narrow passage. Furthermore, an asymmetric state with unequal subchain lengths in the two cavities was more favorable than the symmetric state. The preference for the asymmetric state is driven by the bending energy. Basically, in the symmetric state both subchains are forced to be bent, whereas in the asymmetric case only one of the subchains must bend, leading to an overall smaller bending penalty and overall smaller free energy of the asymmetric state. These results are in contrast to the entropy-controlled partitioning of polymers into confinement and the symmetric translocation state appearing for flexible polymers.     

Free Energy of Polymers Confined in Open and Closed Cavities

Distinct differences between the thermodynamics of open and closed cavities are observed in confinement free energy of macromolecules as a function of chain length and cavity radius and can be of special importance in the case of processes in spatially heterogeneous confinements encountered in various nano‐ and biostructures. In treatments of the confinement free energy, special attention is given to the equilibrium conditions (a full equilibrium for free exchange of macromolecules between cavity and bulk solution or a restricted equilibrium with number of chains in cavity constant) and associated polymer concentration changes. Increased chain stiffness brings about additional effects and complexity, for which the first results are presented here.

     

Simulations of polyelectrolyte dynamics in an externally applied electric field in confined geometry

We consider the dynamics of charged polymers in free solution in a slit geometry under the influence of an electrical field, applied at an angle to the plane parallel walls of the confinement. The simulations are carried out using the Brownian dynamics method with explicit counterions and implicit hydrodynamics. The hydrodynamic interactions between all the particles and the plane parallel walls are taken into account using a diffusion matrix which depends on slit geometry and the actual polyelectrolyte-solute conformations. We observe a selective transport of the charged polymers, as a function of the degree of polymerization and slit height.     

Large blue-shift in the optical spectra of fluorinated polyphenylenevinylenes. A combined theoretical and experimental study

Modifications of the optical properties of poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] induced by fluorination of the vinylene units are investigated by means of time dependent density functional theory (TD-DFT) calculations and spectroscopic measurements in solution. The energy of the main absorption peak is blue-shifted by more than 0.8 eV in the fluorinated polymers. TD-DFT excitation energies for non-fluorinated and fluorinated oligomer structures of increasing number of monomers, employing fully relaxed geometries, are compared to the experimental absorption energies of the polymers. We found that the measured large blue-shift induced by the fluorination of the vinylene units is not caused by the electron-withdrawing effect of the fluorine substituents but it is related to a steric effect. The inter-monomer torsional angle of the fluorinated structures increases above 50 degrees , while in the non-fluorinated systems it is below 20 degrees . Further insight into the origin of the large blue-shift of the excitation energies is gained by a detailed analysis of the torsional potentials of non-fluorinated and fluorinated dihydroxystilbene. While for planar geometries the energy gap increases due to fluorination, it decreases for highly distorted geometries. In addition, we found that the torsional potential of dihydroxystilbene is rather flat, meaning that different isomers might, e.g., in the solid state, coexist.     

Lattice cluster theory of associating polymers. IV. Phase behavior of telechelic polymer solutions

The newly developed lattice cluster theory (in Paper I) for the thermodynamics of solutions of telechelic polymers is used to examine the phase behavior of these complex fluids when effective polymer-solvent interactions are unfavorable. The telechelics are modeled as linear, fully flexible, polymer chains with mono-functional stickers at the two chain ends, and these chains are assumed to self-assemble upon cooling. Phase separation is generated through the interplay of self-assembly and polymer/solvent interactions that leads to an upper critical solution temperature phase separation. The variations of the boundaries for phase stability and the critical temperature and composition are analyzed in detail as functions of the number M of united atom groups in a telechelic chain and the microscopic nearest neighbor interaction energy ε(s) driving the self-assembly. The coupling between self-assembly and unfavorable polymer/solvent interactions produces a wide variety of nontrivial patterns of phase behavior, including an enhancement of miscibility accompanying the increase of the molar mass of the telechelics under certain circumstances. Special attention is devoted to understanding this unusual trend in miscibility.     

Equilibrium of multi-phase systems in gravitational fields

Four necessary conditions for equilibrium of an isolated solid-liquid-vapor system in a gravitational field were derived by Ward and Sasges (1998) in a unified setting, by using an entropy maximization approach, and under the assumption that the liquid-vapor surface tension does not depend on elevation. These are thermal equilibrium, the Laplace and Young equations, and a condition on the chemical potentials of the components present in the system. Gibbs (1876) had obtained the Young equation in a derivation separate from the derivation of the other three conditions and by using an energy minimization approach. However, Gibbs had derived a more general form of the Laplace equation than Ward and Sasges's. Gibbs's equation contained a term expressing the contribution of the variation of surface tension with elevation. This equation has since been neglected by most of the scientific community. In the present paper, the same approach as Ward and Sasges's is used to derive, in an unified setting, the conditions for equilibrium of an isolated solid-liquid-vapor system in a gravitational field but under the assumption that the liquid-vapor surface tension may depend on elevation. The four well-known conditions for equilibrium are obtained, with Gibbs's generalized Laplace equation instead of the classical Laplace equation. The derivations in this paper were carried out for two different system geometries, namely, for a sessile drop and for a conical capillary tube, and similar conditions for equilibrium were obtained.     

Theory of the cooperative transition between two ordered conformations of poly(L-proline). II. Molecular theory in the absence of solvent.

Phenomenological theories of the transition between helical form I (cis peptide bond) and helical form II (trans peptide bond) of poly(-L-proline), which is a typical order in equilibrium order transition, have been presented by Schwarz (using the parameters s, sigma, beta', and beta' in a 2 X 2 matrix formulation) and by the present authors (using the parameters s, sigma betaC, and betaN in a 4 X 4 matrix formulation). A molecular theory of the same transition has been formulated to account for the phenomenological parameters. The statistical weights of regular helical sequences with and without junctions between the two forms were computed from empirical potential energy functions. Two puckering conformations of the pyrrolidine ring, i.e., with the Cgamma atom down and up, were allowed, and the free energy was computed for chains with four types of puckering, viz., regular down, regular up, random A, and random B, in the latter two of which the up and down puckerings were randomly distributed. The random A and random B chains have higher energy than those with regular down or up puckering, in both forms I and II. From both an energetical and a free energetical point of view, form I is more stable than form II under vacuum at room temperature. The dependence of the relative stabilities of form I and form II under vacuum on chain length was examined from both an energy and free energy point of view. The four parameters, s, sigma, beta', and beta', which describe the transitions in Schwarz's theory, were calculated from the statistical weights of various types of sequences. It was found that the thermally induced transition between form I and II under vacuum occurs with the pyrrolidine rings remaining in the down conformation. The calculated values of s suggest that form I is more stable than form II in the regular down chain, while form II is more stable than form I in the regular up chain under vacuum at room temperature. The calculated values of sigma for regular down and regular up pyrrolidine ring puckering are in good agreement with experimental observations, whereas those for random A and random B puckering are much smaller than the experimental values. A theory for the effect of solvent on the parameters s, sigma, beta', and beta' (at constant temperature) is developed, and the computations involving solvent effects are described in the next paper.     

Effect of branching and confinement on star-branched polymeric systems

The effect of confinement, number of branches (functionality), and size of the molecules on various properties as a function of temperature of star-branched polymers confined between two walls was studied using Monte Carlo simulations with the parallel tempering technique. The coil-to-globule transition and the liquidlike to solidlike transition, similar to those observed for linear chains, were characterized in all systems by changes in the heat capacity, internal energy, and radius of gyration. The transitions were also characterized by the most probable isomeric structure at a given temperature. The radius of gyration of the star polymers was smaller than the values of linear chains when the number of arms f increased. For star chains with more than f=5 arms the values of the radius of gyration, and therefore the size of the molecules, were similar for every condition of confinement studied, especially at higher temperatures. As confinement was increased, the difference in the radius of gyration of linear chains and star polymers became even larger. The coil-to-globule transition temperatures shifted to higher temperatures as the size of the chains and the number of arms in a molecule were increased. Effects of confinement were higher on the properties of the system at the smallest separations (less than twice the monomer diameter), where the coil-to-globule transition shifted to lower temperatures. The liquidlike to solidlike transition was present at almost the same temperature for different conditions of confinement, chain size, and number of arms. The behavior of the systems for separations between the walls greater than five bead diameters was similar to the behavior in the unconfined case. Hence, no considerable effect of confinement was found above this separation.