Sampling biases

Fig. 5.15. STM image of a Si (111)-7x7 surface exposed to 0.2 L of O2 at 300 K. The sample bias voltage was 2 V. Dark and bright sites generated by oxygen exposure are marked with A and B, respectively [5.41].

To account for inhomogeneity in bubble sizes, d in Eq. (20-52) should be taken as / Ln,dffLn,d, and evaluated at the top of the vertical column if coalescence is significant in the rising foam. Note that this average d for overflow differs from that employed earlier for S. Also, see Bubble Sizes regarding the correction for planar statistical sampling bias and the presence of size segregation at a wall. 

To assess the well construction materials compatibility versus the subsurface environment and the pesticide of interest, manufacturers can provide data about the various well construction materials or samples can be acquired for laboratory analysis. Also, QC samples of each material can be collected during installation and preserved for laboratory analysis for potential sample bias, if necessary. In addition to well construction materials, the potable water used to clean drilling equipment and to prepare the grout and hydrate bentonite should also be collected for laboratory analysis (see Section 3.2.6). 

Figure 3.7 11x11 nm2 STM image showing the sample bias-dependent imaging of... 

Figure 3.15 SEM images showing the effect of annealing tungsten STM tips using high sample bias (110 V) and tunnelling currents (50 nA). (a) Etched W tip before annealing (b) tip after annealing. (Reproduced from Ref. 38).

Figure 8.9 Dynamics of STM-driven desorption and dissociation of chlorobenzene at Si(lll) (7 x 7) (a) before and (b) after a desorption scan the circles indicate the positions of chlorobenzene molecules before and after desorption (c) appearance of a chlorine adatom formed by dissociation of chlorobenzene with corresponding 3D image (d) measured rates of desorption and dissociation as a function of tunnelling current for a sample bias of + 3 V. (Reproduced from Ref. 26).

Figure 2.5 Schematic representation of the gap of a metal-oxide-vacuum-metal tunneling junction in the case of a low (a) and a high (b) sample bias voltage.

Figure 2.6 (a) Variation in the apparent height of alumina islands on Ni3AI(l 1 1) as a function of sample bias voltage [34],... 

Figure 2.8 Line profiles of the alumina film on Ni3AI(l 1 1) for different sample bias voltages [36],...

As we have seen in the previous chapter, the apparent topography and corrugation of thin oxide films as imaged by STM may vary drastically as a function of the sample bias. This will of course play an important role in the determination of cluster sizes with STM, which will be discussed in the following section. The determination of the size of the metallic nanoparticles on oxide films is a crucial issue in the investigation of model catalysts since the reactivity of the particles may be closely related to their size. Therefore, the investigation of reactions on model catalysts calls for a precise determination of the particle size. If the sizes of the metal particles on an oxidic support are measured by STM, two different effects, which distort the size measurement, have to be taken into account. 

Figure 2.13 STM images of Fe clusters on Al203/Ni3AI(1 1 1) taken for different sample bias voltages. The image size is 48 nm x 48 nm. The labeled particles were used for the evaluation of the particle height and diameter [44].

Figure 3.3 Reaction of a CO molecule released from a CO-terminated tip with an O atom adsorbed on the surface, (a) STM image, taken with a CO-terminated tip, of two O atoms separated by two lattice spacings (2 x 2.89 A) along the [11 0] direction. Grid lines are drawn through the silver surface atoms, (b) Tunneling current during a 1470 mV sample bias pulse with the CO-terminated tip over one of the two O atoms (denoted by Two current rises...

Figure 4.6 Left STM image of a stoichiometric 1 x 1 Ti02(l 1 0) surface, 14A x 14 A. Sample bias + 1.6 V, tunneling current 0.38 nA. The inset shows a ball-and-stick model of the unrelaxed 1 x 1 Ti02(l 1 0) surface. Rows of bridging oxygen atoms are labeled A and rows of fivefold coordinated titaniums B . Right contour plots of [0 1 l]-averaged charge densities associated with electron states within...

Figure 4.10 Simulated STM images (sample bias 1V) at constant density (2.5 x 10-6e/B3) of the (a) hydroxylated and (b) reduced (1 1 0) rutile Ti02 surface (one OH group and one oxygen vacancy, respectively) obtained with B3LYP localized basis set calculation. (Reprinted with permission from Ref. [20].)...

Note that the variance does not depend on the true value x, and the mean estimator x has the least variance. The finite sampling bias is the difference between the estimate x and the true value x, and represents the finite sampling systematic part of the generalized error... 

In the equations above, the mean square error, the sample variance, and the finite sampling bias are all explicitly written as functions of the sample size N. Both the variance and bias diminish as /V — oc (infinite sampling). However, the variance... 

The sample size in a real simulation is always finite, and usually relatively small. Thus, understanding the error behavior in the finite-size sampling region is critical for free energy calculations based on molecular simulation. Despite the importance of finite sampling bias, it has received little attention from the community of molecular simulators. Consequently, we would like to emphasize the importance of finite sampling bias (accuracy) in this chapter. 

In summary, studies carried out with tissue surrogates25 highlight some of the problems that must be overcome before proteins extracted from FFPE tissues can be used for routine proteomic studies. First, these studies demonstrate that reversal of protein-formaldehyde adducts does not assure quantitative extraction of proteins from FFPE tissues or vice-versa. It may ultimately turn out that there is no one universal method that can accomplish both tasks, but that instead, each step will need to be optimized separately. Studies with tissue surrogates also suggest that failure to quantitatively extract the entire protein component from FFPE tissues may result in sampling bias due to the preferential extraction of certain proteins. This behavior may be linked to protein physical properties, such as the isoelectric point. The results of our... 

When the sample is biased positively (Ub > 0) with respect to the tip, as in Fig. 9c, and assuming that the molecular potential is essentially that of the substrate [85], only the normal elastic current flows at low bias (<1.5 V). As the bias increases, electrons at the Fermi surface of the tip approach, and eventually surpass, the absolute energy of an unoccupied molecular orbital (the LUMO at +1.78 V in Fig. 9c). OMT through the LUMO at — 1.78 V below the vacuum level produces a peak in dl/dV, seen in the actual STM based OMTS data for nickel(II) octaethyl-porphyrin (NiOEP). If the bias is increased further, higher unoccupied orbitals produce additional peaks in the OMTS. Thus, the positive sample bias portion of the OMTS is associated with electron affinity levels (transient reductions). In reverse (opposite) bias, as in Fig. 9b, the LUMO never comes into resonance with the Fermi energy, and no peak due to unoccupied orbitals is seen. However, occupied orbitals are probed in reverse bias. In the NiOEP case, the HOMO at... 

Fig. 9 OMT bands for NiOEP, associated with transient reduction (1.78 V) and transient oxidation (—1.18 V). Data obtained from a single molecule in a UHV STM. The ultraviolet photoelectron spectrum is also shown, with the energy origin shifted (by the work function of the sample, as discussed in [25]) in order to allow direct comparison. The highest occupied molecular orbital, n, and the lowest unoccupied molecular orbital, %, are shown at their correct energy, relative to the Fermi level of the substrate. As in previous diagrams,

P + 1.18 V below the vacuum level produces a peak in dl/dV at —1.18 V sample bias. It is also clear from Fig. 9 that there are other occupied MOs, with one near + 1.70 V giving a well-defined shoulder. Note that peaks are observed in dl/dV (and not /). This is because, once current starts to flow through orbital-mediated channels, increasing the bias doesn t turn it off. On the other hand, the probability... 

A noteworthy advance in the design of solution STMs was achieved by Lev et. al. (Lev, 0. Fan, F-R.F. Bard, A.J. J. Electroanal. Chem.. submitted) by including a Pt "flag" electrode in the STM of Fan et. al. (Fan, F-R.F. Bard, A.J. Anal. Chem.. submitted). A battery between the sample and this flag electrode, which remains poised at the rest potential of the solution, enables the sample to be biased away from the rest potential independently of the tip to sample bias. 

Case II Reversible or Ouasi-Reversible Redox Species. If the tip-sample bias is sufficient to cause the electrolysis of solution species to occur, i.e., AEt > AEp, ev, the proximity of the STM tip to the substrate surface (d < 10 A) implies that the behavior of an insulated STM tip-substrate system may mimic that of a two-electrode thin-layer cell (TLC)(63). At the small interelectrode distances required for tunneling, a steady-state concentration gradient with respect to the oxidized (Ox) and and reduced (Red) electroactive species should be established between the tip and the substrate, and the resulting steady-state current will augment that present as a result of the convection of electroactive species from the bulk solution. In many cases, this steady state current is predicted to overwhelm the convective currents, so this situation is of concern when STM imaging under electrochemical conditions (64). 

Lithography With the STM Electrochemical Techniques. The nonuniform current density distribution generated by an STM tip has also been exploited for electrochemical surface modification schemes. These applications are treated in this paper as distinct from true in situ STM imaging because the electrochemical modification of a substrate does not a priori necessitate subsequent imaging with the STM. To date, all electrochemical modification experiments in which the tip has served as the counter electrode, the STM has been operated in a two-electrode mode, with the substrate surface acting as the working electrode. The tip-sample bias is typically adjusted to drive electrochemical reactions at both the sample surface and the STM tip. Because it has as yet been impossible to maintain feedback control of the z-piezo (tip-substrate distance) in the presence of significant faradaic current (vide infra), all electrochemical STM modification experiments to date have been performed in the absence of such feedback control. 

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