Sphere probes

Figure 9.23 Fast (O) and slow (0) mode Dp/Dpo for (a) 14, (b) 47, and (c) 102 nm polystyrene sphere probes in aqueous 700 kDa carboxymethylcellulose, after Delfino, et a/. (38).

The systems studied included (i) 20.4 nm radius carboxylate-modihed polystyrene sphere probes in 2/3 neutralized low-molecular-weight 5 and 150 kDa... 

Phillies, etal. (77) re-examined results of Brown and Zhou(78) and Zhou and Brown (79) on probe diffusion by silica spheres and tracer diffusion of polyisobutylene chains through polyisobutylene chloroform solutions. These comparisons are the most precise available in the literature, in the sense that all measurements were made in the same laboratory using exactly the same matrix polymer samples, and were in part targeted at supporting the comparison made by Phillies, et al.(Jl). Comparisons were made between silica sphere probes and polymer chains having similar Dp and Dt in the absence of polyisobutylene. For each probe sphere and probe chain, the concentration dependence of the single-particle diffusion coefficient is accurately described by a stretched exponential in c. For large probes (160 nm silica spheres, 4.9 MDa polyisobutylene) in solutions of a small (610 kDa) polyisobutylene, Dp c)/Dt(c) remains very nearly independent of c as Dp c) falls 100-fold from its dilute solution limit. 

Experimental investigations of the model system of dye molecules adsorbed onto surfaces of polystyrene spheres have finuly established the sensitivity and surface specificity of the SHG method even for particles of micrometre size [117]. The surface sensitivity of die SHG process has been exploited for probing molecular transport across the bilayer in liposomes [118], for measurement of electrostatic potentials at the surface of small particles [119] and for imaging... 

Figure 2-119. The Connolly surface is determined by inoving a probe sphere (usually a water molecule) over the van der Waals surface. The surface thus obtained is also called the molecular or solvent-encluded surface (see Section 2,10,4 and Figure 2-120).

Tn general, the. solvent-accessible surface (SAS) represents a specific class of surfaces, including the Connolly surface. Specifically, the SAS stands for a quite discrete model of a surface, which is based on the work of Lee and Richards [182. They were interested in the interactions between protein and solvent molecules that determine the hydrophobicity and the folding of the proteins. In order to obtain the surface of the molecule, which the solvent can access, a probe sphere rolls over the van der Waals surface (equivalent to the Connolly surface). The trace of the center of the probe sphere determines the solvent-accessible surjace, often called the accessible swface or the Lee and Richards surface (Figure 2-120). Simultaneously, the trajectory generated between the probe and the van der Waals surface is defined as the molecular or Connolly surface. 

Figure 2-120. The center ofthe rolling probe sphere defines the solvent-accessible surface during movement of the probe over the van der Waals surface. Thus, the molecular surface is expanded by the radius of the solvent molecule,...

Solvent-excluded surfaces correlate with the molecular or Connolly surfaces (there is some confusion in the literature). The definition simply proceeds from another point of view. In this c ase, one assumes to be inside a molecaile and examines how the molecule secs the surrounding solvent molecules. The surface where the probe sphere does not intersect the molecular volume is determined. Thus, the SES embodies the solvent-excluded volume, which is the sum of the van der Waals volume and the interstitial (re-entrant) volume (Figures 2-119. 2-120). 

Fig. l.fi. The van tier Waals (vdw) surface of a molecule corresponds to the outward-facing surfaces of the van der Waak spheres of the atoms. The molecular surface is generated hy rolling a spherical probe (usually of radius 1.4 A to represent a mater molecule) on the van der Wools surface. The molecular surface is consiructed from contact and re-entrant surface elements. The centre of the probe traces out the accessible surface. 

The acce.ssible surface is also widely used. As originally defined by Lee and Richards [Lee and Richai ds 1971] this is the surface that is traced by the centre of the probe molecule as it rolls on the van der Waals surface of the molecule (Figure 1.6). The centre of the probe molecule can thus be placed at any point on the accessible surface and not penetrate the van der Waals spheres of any of the atoms in the molecule. 

The solvent-excluded volume is a molecular volume calculation that finds the volume of space which a given solvent cannot reach. This is done by determining the surface created by running a spherical probe over a hard sphere model of molecule. The size of the probe sphere is based on the size of the solvent molecule. 

Iron(II) ediylenediaminetetraacetic acid [15651 -72-6] Fe(EDTA) or A/,Ar-l,2-ethaiiediylbis[A[-(carboxymethyl)glyciQato]ferrate(2—), is a colorless, air-sensitive anion. It is a good reducing agent, having E° = —0.1171, and has been used as a probe of outer sphere electron-transfer mechanisms. It can be prepared by addition of an equivalent amount of the disodium salt, Na2H2EDTA, to a solution of iron(II) in hydrochloric acid. Diammonium [56174-59-5] and disodium [14729-89-6] salts of Fe(EDTA) 2— are known. 

Advances have been made in directly measuring the forces between two surfaces using freshly cleaved mica surfaces mounted on supports (15), and silica spheres in place of the sharp tip of an atomic force microscopy probe (16). These measurements can be directly related to theoretical models of surface forces. 

Hertzian mechanics alone cannot be used to evaluate the force-distance curves, since adhesive contributions to the contact are not considered. Several theories, namely the JKR [4] model and the Derjaguin, Muller and Torporov (DMT) model [20], can be used to describe adhesion between a sphere and a flat. Briefly, the JKR model balances the elastic Hertzian pressure with attractive forces acting only within the contact area in the DMT theory attractive interactions are assumed to act outside the contact area. In both theories, the adhesive force is predicted to be a linear function of probe radius, R, and the work of adhesion, VFa, and is given by Eqs. 1 and 2 below. 

The second question probes deeper Why do the two electrometer spheres, when charged, exert force on each other What is our explanation of this phenomenon We say that the spheres have an excess of electrons (or protons) and these electrons (or protons) exert force on... 

The reduction ofsec-, and /-butyl bromide, of tnins-1,2-dibromocyclohexane and other vicinal dibromides by low oxidation state iron porphyrins has been used as a mechanistic probe for investigating specific details of electron transfer I .v. 5n2 mechanisms, redox catalysis v.v chemical catalysis and inner sphere v.v outer sphere electron transfer processes7 The reaction of reduced iron porphyrins with alkyl-containing supporting electrolytes used in electrochemistry has also been observed, in which the electrolyte (tetraalkyl ammonium ions) can act as the source of the R group in electrogenerated Fe(Por)R. ... 

Surface forces measurement directly determines interaction forces between two surfaces as a function of the surface separation (D) using a simple spring balance. Instruments employed are a surface forces apparatus (SFA), developed by Israelachivili and Tabor [17], and a colloidal probe atomic force microscope introduced by Ducker et al. [18] (Fig. 1). The former utilizes crossed cylinder geometry, and the latter uses the sphere-plate geometry. For both geometries, the measured force (F) normalized by the mean radius (R) of cylinders or a sphere, F/R, is known to be proportional to the interaction energy, Gf, between flat plates (Derjaguin approximation). 

Sample surfaces are atomically smooth surfaces of cleaved mica sheets for SFA, and various colloidal spheres and plates for a colloidal probe AFM. These surfaces can be modified using various chemical modification techniques, such as Langmuir-Blodged (LB) deposition [12,19] and silanization reactions [20,21]. For more detailed information, see the original papers and references texts. 

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