Monolayer fraction

Support Sbet Loading (mmol V m ) Monolayer fraction Ean (kj mol ln(TOFf... 

Support Sbet (m"g ) Loading (pmolVm ) Monolayer fraction Ea (kJmol ) In(TOF) ... 

Other compounds that preferentially adsorb on the silica gel S sites can interfere with their occupation by azocumene, again causing the rate constants to be higher. For an azocumene monolayer fraction of about 0.019 on PqHi silica, applying about an equal amount of azobenzene increased the rate constant... 

Fig. 3. Effect of monolayer fraction and type of silica on the. 55° first-order rate constants for the thermolysis. Independent variables are purity (Pq, low, and P], high) and density of surface OH groups (Hq, low, and H, high).

As can be seen from Fig. 3, the approximate first-order rate constants depend on the initial fraction of the surface occu])ied by the azocumene. They increase rapidly with monolayer fraction at first, but then level off. This can be most easily e.xplained if the azocumene has preferentially adsorbed on a minority of the silica gel sites that happen to be slow (SI microenvironments for the decomposition reaction. At higher monolayer fractions, th<- S sites are filled and any additional azocumene molecule.s nie forced to occupy different, faster, sites. Apparently most of the sites belong to the faster subspecies, and the nearly level rate constant later in the reaction suggests that these sites do not differ greatly among themselves on a given silica. 

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

Fuerstenau and co-workers observed in the adsorption of a long-chain ammonium ion RNH3 on quartz that at a concentration of 10 Af there was six-tenths of a mono-layer adsorbed and the f potential was zero. At 10 M RNH3, however, the f potential was -60 mV. Calculate what fraction of a monolayer should be adsorbed in equilibrium with the 10 M solution. Assume a simple Stem model. 

Elemental and chemical-state resolution affords the possibility of detecting only a monolayer or even a fraction of a monolayer. This approach is prevalent in PD and in metiiods based on x-ray fluorescence. 

It is thus tempting to define the first saturated layer as being one monolayer, and this often done, causing some confiision. One therefore also often uses tenns like saturated monolayer to indicate such a single adsorbate layer that has reached its maximal two-dimensional density. Sometimes, however, the word saturated is omitted from this definition, resulting m a different notion of monolayer and coverage. One way to reduce possible confiision is to use, for contrast with the saturated monolayer, the tenn fractional monolayer for the tenn that refers to the substrate unit cell rather than the adsorbate size as the criterion for the monolayer density. 

The molecules in an adsorbed layer interact not only with the solid, hut also with their neighbours within the layer. The effect is negligible when the fractional coverage 0 of the surface is small and the adsorbed molecules are therefore far apart, but it becomes increasingly significant as the monolayer becomes more and more crowded. A densely occupied monolayer will act in some degree as an extension of the solid, and will be able to attract further molecules from the gas phase in the manner already described, though more... 

With GIXS facilities at synchrotron radiation sources the structure of fractions of monolayers can be studied, even those of relatively weakly scattering materials. 

In order to demonstrate that the systems in question exhibit nonzero wetting temperature, we have displayed the results of calculations for one of the systems (with =1 at T = 0.7). Fig. 12 testifies that only a thin (monolayer) film develops even at densities extremely close to the bulk coexistence density (p/,(T — 0.7) — 0.001 664). In Fig. 13(a) we show the density profiles obtained at temperature 0.9 evaluated for = 7. Part (b) of this figure presents the fraction of nonassociated particles, x( )- We... 

In the latter the surfactant monolayer (in oil and water mixture) or bilayer (in water only) forms a periodic surface. A periodic surface is one that repeats itself under a unit translation in one, two, or three coordinate directions similarly to the periodic arrangement of atoms in regular crystals. It is still not clear, however, whether the transition between the bicontinuous microemulsion and the ordered bicontinuous cubic phases occurs in nature. When the volume fractions of oil and water are equal, one finds the cubic phases in a narrow window of surfactant concentration around 0.5 weight fraction. However, it is not known whether these phases are bicontinuous. No experimental evidence has been published that there exist bicontinuous cubic phases with the ordered surfactant monolayer, rather than bilayer, forming the periodic surface. 

In the structure with all the surfactant molecules located at monolayers, the volume fraction of surfactant should be proportional to the average surface area times the width of the monolayer divided by the volume, i.e., Ps (X Sa/V. The proportionality constant is called the surfactant parameter [34]. This is true for a single surface with no intersections. In our mesoscopic description the volume is measured in units of the volume occupied by the surfactant molecule, and the area is measured in units of the area occupied by the amphiphile. In other words, in our model the area of the monolayer is the dimensionless quantity equal to the number of amphiphiles residing on the monolayer. Hence, it should be identified with the area rescaled by the surfactant parameter of the corresponding structure. 

FiG. 16 Average Gaussian curvature for 7 = 50 at fixed temperature r = 2.7. is a surfactant volume fraction and a length unit is the size of a surfactant molecule (a bare thickness of the monolayer). 

An analytical solution to this has already been attempted [25]. According to this model, the minimum concentration of fines would be that quantity required to coat each coarse particle with a monolayer of fines. Treating the particles as perfect spheres, the fractional change in combined particle volume due to additional film of fines is then ... 

Standard state unit mole fraction in solution and unit coverage in monolayer. r=-15 °C. 

For below one monolayer the deposit may consist of an inhomogeneous mixture of a bare substrate and clusters approximately one monolayer thick. The state with the lowest chemical potential is represented by a line through the origin and tangent to the E[N) curve near the first local minimum, at Ni Nq. The slope of this tangent defines a chemical potential Thus, as N is increased from 0 to the fraction of the sub-... 

Polyimide-clay nanocomposites constitute another example of the synthesis of nanocomposite from polymer solution [70-76]. Polyimide-clay nanocomposite films were produced via polymerization of 4,4 -diaminodiphenyl ether and pyromellitic dianhydride in dimethylacetamide (DMAC) solvent, followed by mixing of the poly(amic acid) solution with organoclay dispersed in DMAC. Synthetic mica and MMT produced primarily exfoliated nanocomposites, while saponite and hectorite led to only monolayer intercalation in the clay galleries [71]. Dramatic improvements in barrier properties, thermal stability, and modulus were observed for these nanocomposites. Polyimide-clay nanocomposites containing only a small fraction of clay exhibited a several-fold reduction in the... 

As illustrated in Eig. 5.17, we divide the surface into areas that are uncovered (fraction 6q), covered by a single monolayer (0i), two monolayers (62), or by i layers... 

Table S.2. Fraction of empty surface and N2 coverages in one, two, three and four monolayers for the data in Tab. 5.1 and Fig. 5.14 at 61 mbar.

---