Root-mean-square layer thickness

Fig. 10. The root-mean-square layer thickness tms as a function of the square root of chain length r for four values of polymer volume fraction 0 . Hexagonal lattice,...

Two measures of the layer thickness have been widely reported (Takahashi and Kawaguchi, 1982 Cohen Stuart et al, 1986). The root-mean-square layer thickness, defined through... 

Figure 8.10. The normalised root mean square layer thickness for the PS block as a function of the grafting density of a spread film of a PDMS-PS linear diblock copolymer at the surface of ethyl benzoate. After Kent et al. (1995).

The thicknesses of the adsorbed layer can be expressed in terms of the root-mean-square layer thickness... 

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

Scheutjens and Fleer further calculated50 the concentration distributions of loop and tail segments, the root-mean-square thickness of the adsorbed layer, and the average numbers and lengths of trains, loops, and tails. They also computed the distributions of trains, loops, and tails from the free segment probability Pj, which may be represented by... 

Ellipsometry determines a certain average thickness th of the adsorbed layer. However, what is important for the evaluation of polymer conformations in this layer is the root-mean square thickness t. Hence, it is necessary to find a way of relating t to th. McCrackin and Colson66 studied this problem for several distributions of segments and found tnn, = th/l-5 for the exponential distribution and t - th/1.74 for the Gaussian distribution. Takahashi et al.67 showed that t = th/1.63 for the one-train and two-tail model (see Eqs. (B-110) and (B-lll)). 

Fig. 12. Root-mean-square thickness tms of the adsorbed polymer layer vs. polymer concentration70. Symbols are the same as in Fig. 11...

Fig. 13. Root-mean-square thickness t, of the adsorbed polymer layer at the bulk polymer concentration 0.3 g/dl vs. molecular weight70 ...

From studies performed with well characterized substrates and polystyrene with a narrow M distribution, the measured values of T, p, and 0 at the theta point have been found to agree closely with the theories of Silberberg and Scheutjens and Fleer. Furthermore, it has been shown that the measured root-mean-square thickness of the adsorbed layer can be predicted semiquantitatively by the loop-train-tail conformation model. 

Measurements of hydrodynamic thickness LH have been performed by many investigators and, in most cases, the measured LH were almost twice the radii of gyration of polymer coils in bulk solution. It is desirable to clarify the theoretical relationship between LH and the root-mean-square thickness of the adsorbed polymer layer. Some progress in this direction has been made recently. 

One assembly example is polyethylenamine (PEI)-mediated self-assembly of FePt nanoparticles [56]. PEI is an all -NH-based polymer that can replace oleate/oleylamine molecules around FePt nanoparticles and attach to hydrophilic glass or silicon oxide surface through ionic interactions [52], A PEI/FePt assembly is readily fabricated by dipping the substrate alternately into PEI solution and FePt nanoparticle dispersion. Figure 10 shows the assembly process and TEM images of the 4 nm Fes8Pt42 nanoparticle self-assemblies on silicon oxide surfaces. Characterizations of the layered structures with X-ray reflectivity and AFM indicate that PEI-mediated FePt assemblies have controlled thickness and the surfaces of the assemblies are smooth with root mean square roughness less than 2 nm. 

The arrows along the abscissa in fig. 5.19 indicate various layer thicknesses the elllpsometric thickness d . the root-mean-square thickness d , and the hydrodynamic thickness d . For a definition of these quantities we refer to sec. 5.6. From fig. 5.19 it is clear that d " and d are meilnly determined by the loops, whereas measures the extension of the tails. We return to this point below. 

Figures 33.13 shows the topography of the two plasma polymer layers deposited under different conditions on a polished iron surface. Both films show a similar topography as observed by atomic force microscopy, but the film deposited on O2 plasma-pretreated polished iron showed a little more grainy surface than (Ar + H2) plasma-pretreated sample. In Figure 33.14 the root mean square value is plotted against the film thickness. The grainy surface (O2 plasma pretreated), which showed a higher deposition rate, increased the roughness as the thickness increased as expected.

Fundamental frequency of the resonator Correlation function for surface roughness Root mean square height of a roughness Wave vector of shear waves in quartz, (Uy pq//rq Correlation length of surface roughness Thickness of the liquid film Thickness of interfacial layer Molecular dynamics Pressure in a liquid Quartz crystal microbalance Hydrodynamic roughness factor Electrochemical roughness factor Coordinates (normal and lateral)... 

The thickness of the layer may also be defined as a derived parameter fi-om the volume fraction profile c )(z) of the adsorbed polymer layer the most common feature of which is the second moment or root-mean-square thickness of the layer ... 

Fig. 4) can be parametrized by the density pj of each layer, the layer thickness dj and the root-mean-square (rms) roughness q, of each interface with number j (starting from j=0 at zo=0) given by the density probability fimction. This is not necessarily an error-function but could be, for example a tanh-profile for a polymer-polymer interface [6]. However, for the considerations in this chapter the exact form of the profile is not of importance and error-function profiles are assumed. Later on, tanh-profiles are taken for the refinements. 

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