Direct measurement of depletion and hydrodynamic forces in solutions of a reversible supramolecular polymer

In this paper, the investigation of surface forces in semidilute solutions of a nonadsorbing hydrogen-bonded reversible supramolecular polymer is described. Colloidal probe atomic force microscopy was used for direct measurement of depletion forces. Hydrodynamic drag on the AFM cantilever with the colloidal probe was measured both far away from and close to the planar substrate surface. The results indicate that the presence of the depletion layer causes slip at the surfaces with a large apparent slip length. Our analysis explains how the presence of slip enables the measurement of (relatively weak) depletion forces in solutions with a high viscosity by significantly reducing the hydrodynamic forces. The range and magnitude of the measured depletion forces are qualitatively in agreement with previous experiments and theoretical predictions. Due to the relatively large experimental error, no quantitative conclusions can be drawn. Depletion-induced phase separation of suspensions of stearylated silica particles was also observed. Phase separation becomes more pronounced with increasing polymer concentration.     

Equilibration of fluid-phase coexistence in polydisperse particle systems with short- and moderate-range depletion attractions

Gibbs ensemble Monte Carlo (GEMC) simulations have been done on polydisperse systems of particles interacting via the Asakura-Oosawa depletion potential. On restricting the range of the depletion attraction particles aggregate forming long-lived, unequilibrated structures and it becomes increasingly difficult to sample phase space. It is found that by simply equilibrating systems sequentially starting at longer ranges of attraction, the equilibrium fluid-fluid phase coexistence can be determined down to polymer-colloid size ratios approaching 10%. For such short ranges of the depletion interaction it becomes difficult to obtain reliable estimates of chemical potentials due to occasional particle insertions resulting in very low energies. The results show that full equilibrium is not reached at a polymer-colloid size ratio of 10% in spite of lengthy simulations due to persistent structures in the dense-fluid phase dominated by particles belonging to the larger size fraction. Free-volume theory with a polydisperse colloid component, modeled as a three-component mixture, is used for qualitative comparison with some of the results of the computer simulations.     

Direct measurement of forces due to solvent structure

Forces measured between two molecularly smooth solid surfaces separated by inert organic liquids exhibit spatial oscillations with periodicity equal to the size of the liquid molecules. Between five and ten oscillations are measurable, and their amplitude is large compared with the conventional van der Waals force.     

Interaction force between two charged plates immersed in a solution of charged particles. Coupling between double layer and depletion forces

When two parallel plates are immersed in a solution of small charged particles, the center of the particles is excluded from a region of thickness D/2 near the plate, where D is their diameter. The approach which Langmuir developed for the double layer repulsion in the presence of an electrolyte with ions of negligible size is extended to the case in which one of the "ions" is a charged particle of finite, relatively small size. A general expression for the force generated between the two charged plates immersed in an electrolyte solution containing relatively small charged particles is derived. In this expression, only the electrical potential at the middle distance between the plates is required to calculate the force. A Poisson-Boltzmann equation which accounts for the volume exclusion of the charged particles in the vicinity of the surface is solved to obtain the electrical potential at the middle between the two plates. Starting from this expression, some results obtained previously for the depletion force acting between two plates or two spheres are rederived. For charged plates immersed in a solution of an electrolyte and charged small particles, the effects of the particle charge, particle charge sign, particle size, and volume fraction of the particles on the force acting between the two plates are examined.     

Direct measurement of recognition forces between proteins and membrane receptors

The interactions between the protein, cholera toxin B subunit attached to an atomic force microscope, AFM, cantilever, CTB and its receptor the ganglioside, GM1 have been measured in a dilute electrolyte solution, pH 5.5. Although there is variation in the force separation data obtained, particularly on approach of the AFM tip to the GM1 surface where usually, but not always an attraction is noted, an adhesion is always noted on separation of the surfaces. The strength of this adhesion varies from experiment to experiment, but appears to be quantised at a value of around 90 pN. Addition of cholera toxin to the aqueous electrolyte solution completely removes the attractive interaction and adhesion. This gives us confidence that in the earlier experiments, a specific interaction between the CTB and GM1 was measured.     

Direct measurement of weak depletion force between two surfaces

In a mixture of colloidal particles and polymer molecules,the particles may experience an attractive"depletion force"if the size of the polymer molecule is larger than the interparticle separation.This is because individual polymer molecules experience less conformational entropy if they stay between the particles than they escape the inter-particle space, which results in an osmotic pressure imbalance inside and outside the gap and leads to interparticle attraction.This depletion force has been the subject of several studies since the 1980s,but the direct measurement of this force is still experimentally challenging as it requires the detection of energy variations of the order of k_BT and beyond.We present here our results for applying total internal reflection microscopy(TIRM) to directly measure the interaction between a free-moving particle and a flat surface in solutions consisting of small water-soluble organic molecules or polymeric surfactants.Our results indicate that stable nanobubbles(ca.150 nm) exist free in the above aqueous solutions.More importantly,the existence of such nanobubbles induces an attraction between the spherical particle and flat surface.Using TIRM,we are able to directly measure such weak interaction with a range up to 100 nm.Furthermore,we demonstrate that by employing thermo-sensitive microgel particles as a depleting agent,we are able to quantitatively measure and reversibly control k_BYT-scale depletion attraction as function of solution pH.     

Direct observation of substrate-enzyme complexation by surface forces measurement

The substrate-enzyme complexation of heptaprenyl diphosphate synthase was directly investigated using colloidal probe atomic force microscopy (AFM) and a quartz crystal microbalance (QCM) in order to obtain new insights into the molecular mechanism of the enzyme reaction. This enzyme is composed of two dissociable subunits that exhibit a catalytic activity only when they are associated together in the presence of a cofactor, Mg2+, and a substrate, farnesyl diphosphate (FPP). The QCM measurement revealed that FPP was preferentially bound to subunit II in the presence of Mg2+, while the AFM measurement showed that the adhesive force between the subunits was observed only in the presence of both Mg2+ and FPP. This is the first direct demonstration of the specific interaction involved in the enzyme reaction. The dependence of the Mg2+ concentration on the specific interaction between subunits I and II well agreed with that on the enzyme activity of heptaprenyl diphosphate synthase. This indicated that the observed adhesive forces were indeed involved in the catalytic reaction of this enzyme. On the basis of these results, we discussed the processes involved in the substrate-enzyme complexation. The first, the substrate FPP bound to subunit II using Mg2+, followed by the formation of the subunit I-FPP-Mg2+-subunit II complex. Our study showed a very useful methodology for examining the elemental processes of biological reactions such as an enzyme reaction.     

The measurement of forces between particles in disperse systems

Summary An experimental method is described for measuring the forces between particles in a dispersion as a function of the distance of separation of the surfaces. Experimental results have been obtained for plate-like particles, sodium montmorillonite, and spherical particles, polystyrene latices. The force measured was always repulsive. Increasing the concentration of 11 electrolyte from 10^–4 to 10^–1 M, at a constant separation distance for plates and constant volume fraction for spheres, caused a decrease in the force of repulsion between the particles. The experimental results for sodium montmorillonite were compared with theoretical calculations based on a model of two interacting flat plates at constant potential. The experimentally measured repulsion at close distances was higher than that predicted theoretically.

---

Zusammenfassung Eine Methode zur Bestimmung der Kräfte zwischen Teilchen in einer Dispersion in Abhängigkeit vom gegenseitigen Abstand wurde beschrieben. Die experimentellen Resultate wurden mit plättchen-förmigen Teilchen des Natrium-Montmorillonits und kugelförmigen Latexteilchen erhalten. Die ermittelten Kräfte zeigten in allen Fällen die Abstoßung. Bei konstantem Abstand zwischen den Plättchen und bei konstantem Volumenbruch von Kugeln, eine Erhöhung in der Konzentration des 1—1 Elektrolyten von 10^–4 zu 10^–1 M verursachte eine Erniedrigung der Abstoßungskräfte zwischen den Teilchen. Die experimentellen Resultate mit Natrium-Montmorillonit wurden mit den theoretischen Berechnungen für zwei wechselwirkende Plättchen bei konstantem Potential verglichen. Die experimentell bestimmten Abstoßungen bei kleinen Abständen wurden höher als die theoretisch vorausgesagten Werte befunden.

---

---

Plenary lecture by Professor Dr.R. H. Ottewill at the 25th Congress of the Kolloid-Gesellschaft, Munich, October 13–15, 1971.     

Direct measurement of hydrophobic forces on cell surfaces using AFM

Although hydrophobic forces are of great relevance in biological systems, quantifying these forces on complex biosurfaces such as cell surfaces has been difficult owing to the lack of appropriate, ultrasensitive force probes. Here, chemical force microscopy (CFM) with hydrophobic tips was used to measure local hydrophobic forces on organic surfaces and on live bacteria. On organic surfaces, we found an excellent correlation between nanoscale CFM and macroscale wettability measurements, demonstrating the sensitivity of the method toward hydrophobicity and providing novel insight into the nature of hydrophobic forces. Then, we measured hydrophobic forces associated with mycolic acids on the surface of mycobacteria, supporting the notion that these hydrophobic compounds represent an important permeation barrier to drugs.     

Direct measurement of forces between a colloidal particle and a phospholipid bilayer

Colloidal interaction forces between a silica particle and a solid-supported Langmuir-Schaefer phospholipid bilayer were directly measured using a gradient optical trap and evanescent wave light scattering. A small custom-built Langmuir trough was integrated with an optical trapping microscope to allow force measurements on a single particle within the subphase of the trough after the dip of the substrate was completed. The novel method allows the force measurements to be conducted without transferring the substratum across an air/water interface. The fluctuating particle position near the bilayer was tracked by evanescent wave light scattering to determine the deflection due to surface forces, and the relaxation time of particle fluctuations was measured to simultaneously determine the viscous forces. Measured equilibrium and viscous force-distance profiles of silica microspheres with diameters of 1 and 5 microm on bilayers of dipalmitoyl phosphatidyl choline (DPPC) were markedly different than force-distance on bare mica and DPPC monolayers under the same electrolyte conditions.     

Simultaneous measurement of structural and hydrodynamic forces between colloidal surfaces in complex fluids

An AFM study was performed to measure the effect of approach/retraction speed on the interaction force between a colloidal particle and a flat substrate in aqueous solutions containing silica nanospheres at concentrations of 4.5 and 6.5 vol.%. The total force consisted of contributions of electrostatic, depletion, structural and hydrodynamic forces. The hydrodynamic component of the force could be isolated by comparing the force profiles measured upon approach and retraction. It was found that when the hydrodynamic component was subtracted from the total force, the resulting force profiles measured at scan speeds of 80, 800, 2400, 4800 and 11,200 nm/s all overlaid, indicating that the surface forces (electrostatic, depletion and structural) were not affected by the scan speed. This result was further supported by an approximation of the rates of viscous and diffusive motion in the gap region. In addition, the variation of the hydrodynamic force with particle/plate separation distance agreed relatively well with a prediction made using the mobility correction factor developed for simple fluids, suggesting that the nanoparaticles do not alter the flow in the lubrication layer at these concentrations.     

Solvation forces in asymmetrically charged electrolytes

Density functional theories of solvation forces in charged fluids which self-consistently include the effects of finitesized ions are extended to treat asymmetrically charged electrolytes. For a given electrolyte concentration both the electric potential and the solvation force between charged surfaces are seen to deviate from the results of the classical DLVO theory more markedly for asymmetrically charged electrolytes than for a 1 : 1 electrolyte.     

Balance of enthalpy and entropy in depletion forces

Solutes added to solutions often dramatically impact molecular processes ranging from the suspension or precipitation of colloids to biomolecular associations and protein folding. Here we revisit the origins of the effective attractive interactions that emerge between and within macromolecules immersed in solutions containing cosolutes that are preferentially excluded from the macromolecular interfaces. Until recently, these depletion forces were considered to be entropic in nature, resulting primarily from the tendency to increase the space available to the cosolute. However, recent experimental evidence indicates the existence of additional, energetically-dominated mechanisms. In this review we follow the emerging characteristics of these different mechanisms. By compiling a set of available thermodynamic data for processes ranging from protein folding to protein–protein interactions, we show that excluded cosolutes can act through two distinct mechanisms that correlate to a large extent with their molecular properties. For many polymers at low to moderate concentrations the steric interactions and molecular crowding effects dominate, and the mechanism is entropic. To contrast, for many small excluded solutes, such as naturally occurring osmolytes, the mechanism is dominated by favorable enthalpy, whereas the entropic contribution is typically unfavorable. We review the available models for these thermodynamic mechanisms, and comment on the need for new models that would be able to explain the full range of observed depletion forces.     

Direct measurement of interaction forces between a single bacterium and a flat plate

A technique for precisely measuring the equilibrium and viscous interaction forces between a single bacterium and a flat surface as functions of separation distance is described. A single-beam gradient optical trap was used to micromanipulate the bacterium against a flat surface while evanescent wave light scattering was used to measure separation distances. Calibrating the optical trap far from the surface allowed the trapped bacterium to be used as a force probe. Equilibrium force-distance profiles were determined by measuring the deflection of the cell from the center of the optical trap at various trap positions. Simultaneously, viscous forces were determined by measuring the relaxation time for the fluctuating bacterium. Absolute distances were determined using a best-fit approximation to the theoretical prediction for the hindered mobility of a diffusing sphere near a wall. Using this approach, forces in the range from 0.01 to 4 pN were measured at near-nanometer resolution between Staphylococcus aureus and glass that was bare or coated with adsorbed protein.     

Direct measurement of molecular interaction forces in foam films from lung surfactant fraction

Molecular interaction forces, operative in microscopic foam films obtained from the isolated hydrophobic fractions of porcine lung surfactant (AS-B) are investigated by monitoring film thickness h as a function of electrolyte concentration (C _el) and direct measurements of disjoining pressure/thickness (Π(h)) isotherms. The steep decrease of the common film thickness with the increase of C _el evidences the action of long-range electrostatic surface forces. The experimental h(C _el) curve indicates that non-Derjaguin-Landau-Verwey-Overbeek (DLVO) repulsive forces are operative at C _el where common black (CBF) and Newton black films (NBF) are obtained including the physiologically relevant C _el=0.14 mol dm⁻³ NaCl. The action of additional non-DLVO forces is corroborated by the comparison of the experimentally measured Π(h) isotherm with the DLVO theory. Considering the presence of proteins in AS-B and the formation of lipid-protein complexes it is inferred that steric type forces are operative in CBF and NBF.     

Phase coexistence in polydisperse charged hard-sphere fluids: mean spherical approximation

Taking advantage of the availability of the analytic solution of the mean spherical approximation for a mixture of charged hard spheres with an arbitrary number of components we show that the polydisperse fluid mixture of charged hard spheres belongs to the class of truncatable free energy models, i.e., to those systems where the thermodynamic properties can be represented by a finite number of (generalized) moments of the distribution function that characterizes the mixture. Thus, the formally infinitely many equations that determine the parameters of the two coexisting phases can be mapped onto a system of coupled nonlinear equations in these moments. We present the formalism and demonstrate the power of this approach for two systems; we calculate the full phase diagram in terms of cloud and shadow curves as well as binodals and discuss the distribution functions of the coexisting daughter phases and their charge distributions.     

Direct measurement of shear forces between polymer-bearing surfaces sliding past each other

We have used a recently developed surface force balance to measure, with extreme sensitivity, both lateral and normal forces between interacting surfaces, for the case of simple liquids and particularly with surface-attached polymers. The presence of polymers on the surfaces reduces drastically the force required to maintain them in sliding motion, under a given normal load, relative to the bare surface case. We believe this is due to the long range steric repulsion which can sustain a large normal load while maintaining a very fluid interfacial layer. The effect is much more marked for end-tethered chains in a good solvent than for adsorbed chains in a θ-solvent. This is attributed to the different extents of interpenetration of the compressed polymer layers.     

Theory of polydisperse reacting polymer systems

The kinetics of irreversible reactions between polymer chains of different molecular weights are studied, with emphasis on the case of highly reactive end groups. We calculate the rate constant k(N, M) for reaction between chains of lengths N and M respectively, in dilute and semi-dilute solutions and in the melt. In all cases, k(N, M) is dominated by the shortest chain: the limit k(N) ≡ k(N, ∞) is well-defined and scales as if both chains were of length N. In dilute solutions k(N, M) obeys mean field theory, being proportional to the equilibrium reactive group contact probability. For melts and concentrated solutions, k(N, M) follows diffusion-controlled laws: k(N, M) ≈ (R/τ_N)ƒ(M/N) where R_N and τ_N are the coil size and relaxation time of the shortest chain N, and ƒ(M/N) is a cross-over function describing the approach to the asymptotic form k(N) for M/N ≫ 1. We calculate the leading contributions to this cross-over function, which has universal forms depending on the concentration regime. The implications of these results for high-conversion free-radical polymerization are discussed.