Monolayer filling

These limits are somewhat arbitrary pore filling mechanisms also depend on the shapes of the pores and on the size of the adsorptive molecule. Despite this Inherent vagueness, the classification has its use as a first means of discrimination because it points to different pore filling mechanisms macropores are so wide that they behave as "virtually flat" surfaces, mesopores are mainly responsible for capillary condensation, whereas micropores are so narrow that one cannot speak of a macroscopic fluid in them. Because in micropore Jilling adsorbates are only a few layers thick, an adsorption plateau is found suggesting monolayer filling and applicability of the Langmuir or Volmer premises. This mechanism Is distinct from that in meso- and macropores. 

Fig. 4.18 Overlay image of the multichannel chip functionalized with an array of five different fluorescent monolayers filled with acetonitrile (a), Ca2+ (perchlorate salt, 10 4 M, acetonitrile) (b), and Cu2+ (perchlorate salt, 10 4 M, acetonitrile) (c) 68...

The Langmuir isotherm is a local model of the absolute adsorption based on monolayer filling of non-interacting molecules. As such, it represents a model of supercritical adsorption on surfaces. It predicts a monotonically increasing function of pressure, which saturates asymptotically as a function of pressure... 

Figure 22. Submonolayer phase diagram near transiational melting for N2 on graphite the coverage is measured in units of the complete -v/s monolayer. Filled circles Monte Carlo simulations in the NVT ensemble at the coverages 0.2, 0.5, 0.9, 0.93, 0.95, and 1.0. Squares calorimetric measurements [73]. Triangles calorimetric measurements [65]. (Adapted from Fig. 1 of Ref. 103.)...

Fig. X-12. Advancing and receding contact angles of various liquids [water (circles), Gly = glycerol (squares), Form = formamide (diamonds), EG = ethylene glycol (circles), BN = abromonapthalene (squares), BCH = bicyclohexyl (diamond), HD = hexadecane (circles)] on monolayers of HS(CH2)i60R having a range of R groups adsorbed on gold and silver (open and filled symbols respectively). (From Ref. 171.)...

The physical adsorption of gases by non-porous solids, in the vast majority of cases, gives rise to a Type II isotherm. From the Type II isotherm of a given gas on a particular solid it is possible in principle to derive a value of the monolayer capacity of the solid, which in turn can be used to calculate the specific surface of the solid. The monolayer capacity is defined as the amount of adsorbate which can be accommodated in a completely filled, single molecular layer—a monolayer—on the surface of unit mass (1 g) of the solid. It is related to the specific surface area A, the surface area of 1 g of the solid, by the simple equation... 

Examination of these and other results indicates that the value of a for a given adsorptive which needs to be used in order to arrive at a value of specific surface consistent with that from nitrogen adsorption, varies according to the nature of the adsorbent. The existence of these variations shows that the conventional picture, in which the value of a corresponds to a monolayer which is completely filled with adsorbate molecules in a liquidlike packing, is over-simplified. Two factors can upset the simple picture (a) there may be a tendency for adsorbed molecules to become localized on lattice sites, or on more active parts of the solid surface and (b) the process... 

I (curve D). Thus the micropores had been able to enhance the adsorbent-adsorbate interaction sufficiently to replace monolayer-multilayer formation by micropore filling and thereby change the isotherm from being convex to being concave to the pressure axis. 

The first stage in the interpretation of a physisorption isotherm is to identify the isotherm type and hence the nature of the adsorption process(es) monolayer-multilayer adsorption, capillary condensation or micropore filling. If the isotherm exhibits low-pressure hysteresis (i.e. at p/p° < 0 4, with nitrogen at 77 K) the technique should be checked to establish the degree of accuracy and reproducibility of the measurements. In certain cases it is possible to relate the hysteresis loop to the morphology of the adsorbent (e.g. a Type B loop can be associated with slit-shaped pores or platey particles). 

In very small pores the molecules never escape from the force field of the pore wall even at the center of the pore. In this situation the concepts of monolayer and multilayer sorption become blurred and it is more useful to consider adsorption simply as pore filling. The molecular volume in the adsorbed phase is similar to that of the saturated Hquid sorbate, so a rough estimate of the saturation capacity can be obtained simply from the quotient of the specific micropore volume and the molar volume of the saturated Hquid. 

Fig. 11. versus P data and contact hysteresis reported by Chaudhury and Whitesides [471. (a) The data for unmodified PDMS-PDMS contacts. No contact hysteresis was observed, (b) The data for and PDMS modified with alkyl siloxane monolayers, PDMS° -03Si(CH2)9CH3. A weak contact hysteresis was observed, (c) The data for PDMS modified with fluroalkyl siloxane monolayers, PDMS -03Si(CH2)2(CF2)7CF3. A large contact hysteresis was observed. In all cases, the open circles represent the loading data, and the filled circles represent the unloading data. 

The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. 

Animal cell cultures that are initiated from cells removed directly from the animal are called primary cultures (Figure 2). Primary cultures include both explant cultures (i.e., cultures initiated from small pieces of intact tissue), as well as cultures initiated from preparations of individual or dispersed cells (obtained from intact tissue by mechanical or proteolytic dismption). Nerve fiber explant cultures in blood plasma were among the earliest types of tissue cultures (Harrison, 1907). Cells grow out from such tissue explants and form a single layer of cells completely filling the tissue culture vessel surface. Such cell cultures are called confluent monolayers. Confluent monolayers can then be treated with trypsin, so as to remove the individual cells from the culture vessel surface. The resulting cell suspension is then transferred into other culture containers, so that more viable monolayer... 

FIG. 24 Monolayer G-LE coexistence conditions from the simulations of Siepmann et al. (Ref. 369) on a pentadecanoic acid model using Gibbs ensemble Monte Carlo simulation. The filled circles are the simulation results. Experimental results are also shown from Ref. 370 (triangles), Ref. 14 (squares), and Ref. 15 (diamonds). (Reproduced with permission from Ref. 369. Copyright 1994 American Chemical Society.)... 

As in a monolayer adsorption process, we consider that the rate of filling of sites by TCP molecules follows first-order kinetics. If No represents the total number of free sites per unit area at time t = 0, and N(t) is the number of sites available at time t, then dN(t)ldt = -kN(t), where k is the rate constant of the adsorption process. Therefore, N(t) decreases as No exp(-kt), and the number of sites occupied by TCP molecules at t becomes [No -N(t)], a quantity that determines directly the parameter (t) in Eq. (25). So Wo(t) can be written as... 

Figure 5.19 shows an idealized form of the adsorption isotherm for physisorption on a nonporous or macroporous solid. At low pressures the surface is only partially occupied by the gas, until at higher pressures (point B on the curve) the monolayer is filled and the isotherm reaches a plateau. This part of the isotherm, from zero pressures to the point B, is equivalent to the Langmuir isotherm. At higher pressures a second layer starts to form, followed by unrestricted multilayer formation, which is in fact equivalent to condensation, i.e. formation of a liquid layer. In the jargon of physisorption (approved by lUPAC) this is a Type II adsorption isotherm. If a system contains predominantly micropores, i.e. a zeolite or an ultrahigh surface area carbon (>1000 m g ), multilayer formation is limited by the size of the pores. 

Here the phenomenon of capillary pore condensation comes into play. The adsorption on an infinitely extended, microporous material is described by the Type I isotherm of Fig. 5.20. Here the plateau measures the internal volume of the micropores. For mesoporous materials, one will first observe the filling of a monolayer at relatively low pressures, as in a Type II isotherm, followed by build up of multilayers until capillary condensation sets in and puts a limit to the amount of gas that can be accommodated in the material. Removal of the gas from the pores will show a hysteresis effect the gas leaves the pores at lower equilibrium pressures than at which it entered, because capillary forces have to be overcome. This Type IV isotherm. 

STM studies of the Au(llO) surface indicated that only the Se (2x3) structure was formed at coverages much below one monolayer and that it was formed homogeneously. At monolayer and higher coverages, a honeycomb structure composed of chains of Se atoms was observed, which at still higher coverages filled in to complete a second Se layer. 

Figure 9.15 Kinetic current density (squares) at 0.8 V for O2 reduction on supported Pt monolayers in a 0.1 M HCIO4 solution, and the calculated activation energy barriers for O2 dissociation (filled circles) and OH formation (open circles) on PtML/Au(lll), Pt(lll), PtML/ Pd(lll), and PtML/lT(lll). as a function of the calculated binding energy of atomic oxygen (BEo). The current density data for Pt(lll) were obtained fiom [Maikovic et al., 1999] and ate included for comparison. Key 1, Pt]y[L/Ru(0001) 2, Pb /bllll) 3, PtML/Rh(lH)i 4, Ptim,/ Au(lll) 5, Pt(lll) 6, PtML/Pd(lll). Surface coverage is ML O2 in O2 dissociation and ML each for O and H in OH formation. (Reproduced with permission fiom Zhang et al. [2005a].)...

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