Force measurements

95xl03 E066/pdd (SI units). Robinson and Jones (1980, 1981) observed that the angle of repose of a packed bed increased monotomically up to 90 ° with applied electric fields up to 3 kV/cm in the bed. They observed a similar field dependence for glass spheres of 75-125 pm and 600-710 pm but almost no effect on 1500-2000 pm particles. 

FIGURE 3-16 Experimental configurations used for the measurement of powder forces (vibration-shear cell-impaction) with electrostatic effect added. 

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Typical correlation between the magnetic characteristic and the body force measured on the head of 85 mm long M24 Friedberg 10.9 bolts where the thickness off the plates screwed together is more than 40mm. 

A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. 

Fig. VI-4. Illustration of the surface force apparatus with the crossed-cylinder geometry shown as an inset. The surface separations are determined from the interference fringes from white light travelling vertically through the apparatus. At each separation, the force is determined from the deflection in the force measuring spring. For solution studies, the entire chamber is filled with liquid. (From Ref. 29.)...

AFM Atomic force microscopy [9, 47, 99] Force measured by cantilever deflection as probe scans the surface Surface structure... 

Protein adsorption has been studied with a variety of techniques such as ellipsome-try [107,108], ESCA [109], surface forces measurements [102], total internal reflection fluorescence (TIRE) [103,110], electron microscopy [111], and electrokinetic measurement of latex particles [112,113] and capillaries [114], The TIRE technique has recently been adapted to observe surface diffusion [106] and orientation [IIS] in adsorbed layers. These experiments point toward the significant influence of the protein-surface interaction on the adsorption characteristics [105,108,110]. A very important interaction is due to the hydrophobic interaction between parts of the protein and polymeric surfaces [18], although often electrostatic interactions are also influential [ 116]. Protein desorption can be affected by altering the pH [117] or by the introduction of a complexing agent [118]. 

The flotation of mica has been correlated to the adhesion force measured from surface force (SFA—see Section VI-4) experiments although, to these authors, it is clear that dynamic effects prevent an absolute comparison [69, 70],... 

Craig V S J 1997 An historical review of surface force measurement techniques Colloids Surf. A Physicochem. Eng. Aspects 129-30 75... 

Thundat T, Zheng X-Y, Chen G Y, Sharp S L, Warmack R J and Schowalter L J 1993 Characterization of atomic force microscope tips by adhesion force measurements App/. Phys. Lett. 63 2150... 

Larson I, Drummond C J, Chan D Y C and Grieser F 1993 Direct force measurements between TI02 surfaces J. Am. Chem. Soc. 11511 885... 

Compared witii other direct force measurement teclmiques, a unique aspect of the surface forces apparatus (SFA) is to allow quantitative measurement of surface forces and intermolecular potentials. This is made possible by essentially tliree measures (i) well defined contact geometry, (ii) high-resolution interferometric distance measurement and (iii) precise mechanics to control the separation between the surfaces. 

One of the most important extensions is the measurement of lateral forces (friction). Friction measurements have accompanied tlie SFA teclmique since its early begiimings in the Cavendish laboratory in Cambridge [37] and a variety of different lateral force measurements are practised throughout tlie SFA conmumity. 

Figure Bl.20.1. Direct force measurement via deflection of an elastic spring—essential design features of a direct force measurement apparatus.

In accordance with equation (Bl.20.1). one can plot the so-called surface force parameter, P = F(D) / 2 i R, versus D. This allows comparison of different direct force measurements in temis of intemiolecular potentials fV(D), i.e. independent of a particular contact geometry. Figure B 1.20.2 shows an example of the attractive van der Waals force measured between two curved mica surfaces of radius i 10 nun. 

Figure Bl.20.8. DLVO-type forces measured between two silica glass surfaces in aqueous solutions of NaCl at various concentrations. The inset shows the same data in the short-range regime up to D = 10 mn. The repulsive deviation at short range (<2 nm) is due to a monotonic solvation force, which seems not to depend on the salt concentration. Oscillatory surface forces are not observed. With pemiission from [73].

Figure Bl.20.9. Schematic representation of DLVO-type forces measured between two mica surfaces in aqueous solutions of KNO3 or KCl at various concentrations. The inset reveals the existence of oscillatory and monotonic structural forces, of which the latter clearly depend on the salt concentration. Reproduced with pennission from [94].

Interactions between macromolecules (protems, lipids, DNA,.. . ) or biological structures (e.g. membranes) are considerably more complex than the interactions described m the two preceding paragraphs. The sum of all biological mteractions at the molecular level is the basis of the complex mechanisms of life. In addition to computer simulations, direct force measurements [98], especially the surface forces apparatus, represent an invaluable tool to help understand the molecular interactions in biological systems. 

Kelly T W ef a/1998 Direct force measurements at polymer brush surfaces by atomic force microscopy Macromoiecuies 31 4297-300... 

Leckband D ef a/1994 Direct force measurements of specific and nonspecific protein interactions S/oc/rem/sfry 33 4611-23... 

A wide variety of measurements can now be made on single molecules, including electrical (e.g. scanning tunnelling microscopy), magnetic (e.g. spin resonance), force (e.g. atomic force microscopy), optical (e.g. near-field and far-field fluorescence microscopies) and hybrid teclmiques. This contribution addresses only Arose teclmiques tliat are at least partially optical. Single-particle electrical and force measurements are discussed in tire sections on scanning probe microscopies (B1.19) and surface forces apparatus (B1.20). 

Apart from the development of imaging and force measurement devices, an important biophysico-chemical problem is... 

In this section we describe the behavior of a ligand subjected to three types of external forces a constant force, forces exerted by a moving stiff harmonic spring, and forces exerted by a soft harmonic spring. We then present a method of reconstruction of the potential of mean force from SMD force measurements employing a stiff spring (Izrailev et al., 1997 Balsera ct al., 1997). 

Stiff Spring For a stiff spring, satisfying K (fiUjdx, under the overdamped condition assumed in (3) the average force measured by the spring can be expressed as... 

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. 

A Procedurefor the Specijication, Calibration and Testing of Strain Gage Eoad Cells for Industrial Process Weighing and Force Measurement, Institute of Measurement and Control, London. 

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