Matrix crack deflection at an interface between a stiff matrix and a soft inclusion

Matrix crack deflection by an interface increases the apparent toughness of a composite. Criteria developed to predict such a mechanism never gave a complete and satisfying answer. They require additional assumptions on a characteristic fracture length and are sensitive to these choices. The criterion proposed here is based on the maximum total energy decrease, it is independent of any length and is well-suited to study a stiff matrix crack impinging on a soft inclusion.     

Relative rotational motion between alpha-Cyclodextrin Derivatives and a stiff axle molecule

Novel [2]rotaxanes bearing alpha-cyclodextrin (alpha-CD) derivatives and a diphenylacetylene axis molecule with trinitrobenzene as a bulky stopper have been prepared to investigate the relative rotary movement of a ring relative to an axis molecule and that of an axis molecule in a ring by NMR techniques. [2]Rotaxanes 2 and 3 were composed of alpha-CD derivatives (2: 6-phenyl-amide-alpha-CD; 3: 6-stilbene-amide-alpha-CD). The protons of alpha-CDs in rotaxanes were thoroughly assigned by the two-dimensional NMR techniques (TOCSY, COSY, ROESY, HMQC, and HMBC). The protons of alpha-CD in rotaxane 1 did not show splitting, whereas the resonance peak shifts and splitting for the corresponding protons of alpha-CD derivatives in rotaxanes 2 and 3 were observed by the shielding and deshielding effects from a diphenylacetylene axis molecule. The splitting of resonance peaks was closely related to the rotary movements of alpha-CDs and an axis molecule. We supposed that alpha-CD in rotaxane 1 rotates freely around a diphenylacetylene axis molecule, and vice versa, whereas the rotary movement of alpha-CD derivatives and the axis molecules of rotaxanes 2 and 3 were restricted by the steric repulsion between the substituent group of alpha-CD and the stopper group of an axis molecule. To estimate the relative rotary movement of CDs and an axis molecule in rotaxanes, the rotational correlation time (tauc) of rotaxanes was measured by 13C NMR. The results indicate that the corresponding rotary movement of the modified alpha-CD and the axis molecules in rotaxanes 2 and 3 depends on the size of the substituent group.     

Unconventional salt trend from soft to stiff in single neurofilament biopolymers

We present persistence length measurements on neurofilaments (NFs), an intermediate filament with protruding side arms, of the neuronal cytoskeleton. Tapping mode atomic force microscopy enabled us to visualize and trace at subpixel resolution photoimmobilized NFs, assembled at various subunit protein ratios, thereby modifying the side-arm length and chain density charge distribution. We show that specific polyampholyte sequences of the side arms can form salt-switchable intrafilament attractions that compete with the net electrostatic and steric repulsion and can reduce the total persistence length by half. The results are in agreement with present X-ray and microscopy data yet present a theoretical challenge for polyampholyte interchain interactions.     

Forces between a Rigid Probe Particle and a Liquid Interface

The effect of disjoining pressure between a rigid spherical probe particle (attached to an AFM cantilever) and a liquid interface (e.g., oil/water or air/water) is treated in an analytic manner to describe the total force F exerted on the probe as a function of the distance X of the probe from the rigid substrate (AFM stage) on which the liquid interface resides. Two cases (i) a flat interface under gravity and (ii) a drop whose size is sufficiently small that gravity can be neglected have been examined. A simple numerical algorithm is given for computing F(X) (the AFM observable) from a given form for the disjoining pressure. Numerical results are displayed for electrostatic probe/interface interactions which reveal the linear compliance regime experimentally observed in AFM experiments on these systems. The slope of the linear compliance regime is shown to be a function of the properties of the interface (capillary length, particle radius, drop size, contact angle of drop on rigid substrate etc.). Copyright 2001 Academic Press.     

Statistics of stiff polymer chains near an adsorbing surface

The exact solution of the problem of adsorption of a long ideal polymer chain with variable degree of stiffness on a plane surface is presented. It is shown that the adsorption of stiff polymer chains is a second-order phase transition; in the adsorbed state “train” (i.e. adsorbed) sections are relatively longer and loop sections relatively shorter than for flexible chains. This effect is very pronounced: already for moderately stiff chains the number of Kuhn segment lengths in one “train” section at the temperature T = T_cr/2 (T_cr is the critical temperature for adsorption transition) can reach several thousands, and deviation from the surface occurs only in the form of small “hairpins”. The maximum length of the chain, which at the given conditions would flatten completely on the surface, is estimated.     

Forces between cylindrical nanoparticles in a liquid crystal

Using classical density functional theory, the forces between two cylindrical nanoparticles in a liquid crystal solvent are calculated. Both the nematic and isotropic phases of the solvent are considered. In the nematic phase, the interaction is highly anisotropic. At short range, changes in the defect structure around the cylinders leads to a complex interaction between them. In the isotropic phase, an attractive interaction arises due to overlap between halos of ordered fluid adsorbed on the surfaces of the cylinders.     

Forces between surfaces in liquids

The results and implications of direct force measurements between molecularly smooth mica surfaces in liquids are reviewed. These discussions include four interactions fundamental to colloid science: van der Waals forces, double layer forces, adhesion forces and structural or solvation forces (e.g. hydration forces). Also considered are the effects of preferential surface adsorption of solute molecules on these interactions, e.g. surfactant adsorptions from aqueous solutions and water condensation from non-aqueous solvents.In aqueous media it is apparent that the DLVO theory is valid at all surface separations down to the “force barrier”, but that under certain conditions hydration forces can become significant at distances below 30 Å.The measured adhesion force between two solid surfaces can be simply related to their surface energies and where meniscus forces are also present due to “capillary condensation” from vapor solvent, their effect on adhesion can be understood in terms of straightforward bulk thermodynamic principles. Here, too, it is concluded that structural forces cannot be ignored.Our results suggest that structural forces may either very monotonically with distance or be oscillatory with a periodicity equal to the molecular size. Their origin, nature, mode of action and importance for particle interactions will no doubt take many years to sort out.     

Forces between Polymer Surfaces and Self-Assembled Monolayers

Gold-coated atomic force microscope (AFM) tips functionalized with amine-, hydroxyl-, carboxylic acid-, and methyl-terminated alkanethiol molecules were used to probe the adhesive forces of polystyrene and poly(acrylic acid) films in dry air (relative humidity < 0.5%). X-ray photoelectron spectroscopy (XPS) and contact angle measurements confirmed the quality and uniformity of similarly treated gold surfaces and the polymer films. XPS indicated that the amine-functionalized thiol films were protonated and comprised of multilayers. Contact angle data were used to calculate surface free energies, and DMT theory yielded the works of adhesion and interfacial free energies for the tip-substrate combinations. In the case of polystyrene, the work of adhesion followed the order methyl > carboxylic acid > hydroxyl > amine. For poly(acrylic acid), the observed order was hydroxyl > amine > carboxylic acid > methyl.     

Forces between nanorods with end-adsorbed chains in a homopolymer melt

Adsorbed or grafted polymers are often used to provide steric stabilization of colloidal particles. When the particle size approaches the nanoscale, the curvature of the particles becomes relevant. To investigate this effect for the case of cylindrical symmetry, I use a classical fluids density functional theory applied to a coarse-grained model to study the polymer-mediated interactions between two nanorods. The rods are coated with end-adsorbing chains and immersed in a polymer melt of chemically identical, nonadsorbing chains. The force between the nanorods is found to be nonmonotonic, with an attractive well when the two brushes come into contact with each other, followed by a steep repulsion at shorter distances. The attraction is due to the entropic phenomenon of autophobic dewetting, in which there is a surface tension between the brush and the matrix chains. These results are similar to previous results for planar and spherical polymer brushes in melts of the same polymer. The depth of the attractive well increases with matrix chain molecular weight and with the surface coverage. The attraction is very weak when the matrix chain molecular weight is similar to or smaller than the brush molecular weight, but for longer matrix chains the magnitude of the attraction can become large enough to cause aggregation of the nanorods.     

Forces between surfaces in electrolyte solutions

Density functional theories of solvation forces in charged fluids are extended to treat electrolytes consisting of finitesized ions and neutral solvent particles. The resulting forces display pronounced oscillations whose magnitude is a strong function of the bulk density of the neutral species.     

Interaction Forces between Hydrophobic and Hydrophilic Self-Assembled Monolayers

An investigation is presented of the interaction of charged self-assembled monolayers (SAMs) with a monoprotic ionizable acid functional group (-COOH) and uncharged SAMs with a methyl terminated functional group (-CH(3)). The strength of the interactions are determined using an atomic force microscope. For all electrolyte conditions investigated the interactions are not well described by a summation of van der Waals attractions and electrostatic repulsions in a manner suggesting that van der Waals attractions are screened. The repulsions are accurately described as corresponding to two surfaces of different charge interacting with surface charges that are independent of separation (i.e., the constant charge model). A small adhesion force was observed under all conditions and its magnitude increased with NaCl concentration. Copyright 2000 Academic Press.     

Forces between thiolate-modified gold surfaces in a melt of end-functionalized polymers

To better understand surface forces across polymer melts, we measured the force between two chemically well-defined solid surfaces in a melt of polymer chains with a functional end group. As for surfaces, we used self-assembed monolayers (SAMs) of alkyl thiols with different end groups (methyl, amino, and hydroxyl) on gold. The polymer was a hydroxyl-terminated polyisoprene. To measure the force, an atomic force microscope was used. Between methyl-terminated SAMs, a weak and short-range repulsion was detected. Between hydroxyl or amino-terminated SAMs, a strong and long-range repulsion was observed up to distances of 16 nm. This indicates that the hydroxyl group of the polymer binds to the hydroxyl or amino groups of the SAMs. It forms a brush-like structure, which leads to steric repulsion. On amino-terminated SAMs, force-versus-distance curves on approach and retraction were monotonically repulsive and reversible. With hydroxyl-terminated SAMs, a jump was observed on approach when the load exceeded a certain threshold. On retraction, an adhesion had to be overcome. We interpret the jump as a rupture of the polymer layer. It indicates that the kinetics of bond and brush formation is faster on OH-SAMs than on NH2-SAMs.     

Electrostatic interaction between a cylinder and a planar surface

 An exact analytical expression for the potential energy of the electrostatic interaction between a plate-like particle 1 and a cylindrical particle 2 of radius a ₂ immersed in an electrolyte solution of Debye–Hückel parameter κ is derived on the basis of the linearized Poisson–Boltzmann equation without recourse to Derjaguin's approximation. Both particles may have either constant surface potential or constant surface charge density. In the limit of κa ₂→0, in particular, the interaction between a plate with zero surface charge density and a cylinder having constant surface charge density becomes identical to the usual image interaction between a line charge (a charged rod of infinitesimal thickness) and an uncharged plate. Received: 22 September 1998  Accepted in revised form: 27 January 1999     

Site-selective surface modification using enzymatic soft lithography

Surface modification with functional polymers or molecules offers great promise for the development of smart materials and applications. Here, we describe a versatile and easy-to-use method of site-selective surface modification based on the ease of microcontact printing and the exquisite selectivity of enzymatic degradation. A micropatterned poly-L-lysine (PLL) layer on solid substrates was prepared by enzymatic degradation using trypsin enzyme immobilized on a prestructured poly(dimethlylsiloxane) (PDMS) stamp. After the enzymatic degradation of PLL and the removal of the degradation products, very well defined patterning was revealed over a large scale by fluorescence microscopy and atomic force microscopy (AFM). We investigate the advantage of our method by comparison with traditional microcontact printing and found that lateral diffusion was reduced, yielding a more accurate reproduction of the master. We also demonstrate that the stamp can be reused without reinking. The patterned surface was used for site-selective modification. The strategy was applied to two applications: the first is dedicated to the creation of amino-silane patterned surfaces, and the second illustrates the possibility of patterning polyelectrolyte multilayered thin films.     

Forces between a rigid probe particle and a liquid interface. II. The general case

The semianalytic theory developed previously (Chan, D. Y. C., Dagastine, R. R., and White, L. R., J. Colloid Interface Sci. 236, 141 (2001)) to predict the force curve of an AFM measurement at a liquid interface using a colloidal probe has been expanded to incorporate a general force law with both attractive and repulsive forces. Expressions for the gradient of the force curve are developed to calculate the point at which the probe particle on the cantilever will spontaneously jump in toward the liquid interface. The calculation of the jump instability is reduced to a straightforward embroidery of the simple algorithms presented in Chan et al. In a variety of sample calculations using force laws including van der Waals, electrostatic, and hydrophobic forces for both oil/water and bubble/water interfaces, we have duplicated the general behaviors observed in several AFM investigations at liquid interfaces. The behavior of the drop as a Hookean spring and the numerical difficulties of a full numerical calculation of F(deltaX) are also discussed.     

Forces between two polymer layers adsorbed at a solid-liquid interface in a poor solvent

The forces between mica surfaces a distance D apart immersed in cyclohexane, bearing adsorbed layers of polystyrene, have been measured at temperatures lower than the corresponding critical temperatures. Polymers of two different molecular weights were used. The results show that these forces are attractive for 3R_g > D >. R_g (where R_g is the polymer radius of gyration) and repulsive at lower D, and may be understood in terms of the phase equilibrium of the polystyrene-cyclohexane system. The adsorption of the polymer under these conditions appears to be effectively irreversible over the time of our experiments. The adsorbance of polymer and the thickness of the adsorbed layers are comparable with values measured in other studies using entirely different techniques.     

Discrete charge effects on the Donnan potential and surface potential of a soft particle

The Donnan potential and surface potential of soft particles (i.e., polyelectrolyte-coated hard particles) in an electrolyte solution play an essential role in their electric behaviors. These potentials are usually derived via a continuum model in which fixed charges inside the surface layer are distributed with a continuous charge density. In this paper, for a plate-like soft particle consisting of a cubic lattice of fixed point charges, on the basis of the linearized Poisson–Boltzmann equation, we derive expressions for the electric potential distribution in the regions inside and outside the surface layer. This expression is given in terms of a sum of the screened Coulomb potentials produced by the point charges within the surface layer. We show that the deviation of the results of the discrete charge model from those of the continuous charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large.     

Donnan potential and surface potential of a spherical soft particle in an electrolyte solution

A simple numerical method, which does not involve numerical integration of the Poisson-Boltzmann equations, is presented for obtaining the relationship between the Donnan potential and surface potential of a spherical soft particle (i.e., a polyelectrolyte-coated particle) in a symmetrical electrolyte solution. We assume that a soft particle consists of the particle core of radius a covered with an ion-penetrable surface layer of polyelectrolytes of thickness d and that ionized groups of valence Z are distributed at a uniform density of N in the polyelectrolyte layer and the relative permittivity takes the same value in the regions outside and inside the polyelectrolyte layer. The Donnan potential and surface potential are determined by the values of a, d, Z, N, and the Debye-Hückel parameter kappa of the electrolyte solution. Numerical results obtained by the present method are in excellent agreement with exact results obtained by solving the nonlinear spherical Poisson-Boltzmann equations for the both regions inside and outside the polyelectrolyte layer.     

Ion-specific forces between a colloidal nanoprobe and a charged surface

We investigate the effect of ion-specific potentials on the force between a nanoprobe attached to a cantilever tip, and a charged surface. The probe is treated as a spherical nanoparticle with constant charge. A modified Poisson-Boltzmann equation in bispherical coordinates is used to address this problem in a more quantitative way. We predict that the ion-specific series of measured forces depend on the sign and magnitude of surface charge densities.