Monolayer Relaxation

Relaxation of the Chemical Bond, Springer Series in Chemical Physics 108, DOI 10.1007/978-981-1585-21-7 12, Springer Science+Business Media Singapore 2014 

Where do and dj are the bond lengths for atoms inside the bulk and for atoms at the surface, 

However, the d 2 of the hcp(OOOl) surface of Be and Mg and the dimer bonds of the Il-b elements of Zn, Cd, and Hg have been reported to expand. With a reduction in Se grain size from 70 to 13 nm, the a lattice was found to expand by 0.3 %, but the c lattice spacing decreases shghtly, which expands the unit-cell volume by about 0.7 % at D = 13 nm [13]. The reported expansion appears off line with notations of Goldschmidt and Pauling who emphasized that the global bond contraction depends uniquely on the reduction in atomic CN, and it is independent of the bond namre or the particular constituent elements (Appendix A2) (Table 12.2). 

Metal Method Adi2 di2 Metal Method Adl2 dl2 (%) 

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An HM-HEC monolayer at the air/aqueous interface was formed by adsorption from an aqueous solution of the polymer placed in the Langmuir trough overnight. In "stress-jump" experiments, HM-HEC monolayers were placed under rapid compression to a large degree and surface pressure was measured as a function of time after compression was stopped. (The compressional "jumps" required a minute or two to complete, and in some cases were on the order of the polymer monolayer relaxation times. See later section for discussion). In hysteresis experiments, the adsorbed monolayers were subjected to continuous compression-expansion cycles at a specific speed, while surface pressure was determined as a function of surface area. 

Table 1 Fit of monolayer relaxation to double exponential. Parameters used to fit R versus t data in Fig. 10 to a double exponential decay, i.e. An =bySsp tlzy) +62 (t/tj). SE = standard error, CV% = confidence value (%)...

Then let us examine the rate relaxation time constant x, defined as the time required for the rate increase Ar to reach 63% of its steady state value. It is comparable, and this is a general observation, with the parameter 2FNq/I, (Fig. 4.13). This is the time required to form a monolayer of oxygen on a surface with Nq sites when oxygen is supplied in the form of 02 This observation provided the first evidence that NEMCA is due to an electrochemically controlled migration of ionic species from the solid electrolyte onto the catalyst surface,1,4,49 as proven in detail in Chapter 5 (section 5.2), where the same transient is viewed through the use of surface sensitive techniques. 

During an XAS experiment, core electrons are excited. This produces empty states called core holes. These can relax by having electrons from outer shells drop into the core holes. This produces fluorescent X-rays that have a somewhat lower energy than the incident X-rays. The fluorescent signal is proportional to the absorption. Detection of this signal is a useful method for measuring absorption by dilute systems such as under potential deposited (UPD) monolayers. 

After addition of lipid DSPC into the organic phase a monolayer is formed at the interface, and the steady-state current increased at all potentials. On expansion, the time constant of the charging current is reduced to ca. 5 ms and a shift of ca. 100 mV is observed in the potential of zero charge. From the video image of the droplet a highly distorted and heterogeneous interface is seen which relaxes after the fast stage (a few... 

The measured NMR signal amplitude is directly proportional to the mass of adsorbate present, and the NMR signal versus pressure (measured at a fixed temperature) is then equivalent to the adsorption isotherm (mass of adsorbate versus pressure) [24-25]. As in conventional BET measurements, this assumes that the proportion of fluid in the adsorbed phase is significantly higher than the gaseous phase. It is therefore possible to correlate each relaxation time measurement with the calculated number of molecular layers of adsorbate, N (where N = 1 is monolayer coverage), also known as fractional surface coverage. 

Fig. 3.5.4 Spin-lattice relaxation (normalized to the bulk gas f at the same pressure) as a function of fractional surface coverage (i.e., the number of adsorbate monolayers).

The difference between the static or equilibrium and dynamic surface tension is often observed in the compression/expansion hysteresis present in most monolayer Yl/A isotherms (Fig. 8). In such cases, the compression isotherm is not coincident with the expansion one. For an insoluble monolayer, hysteresis may result from very rapid compression, collapse of the film to a surfactant bulk phase during compression, or compression of the film through a first or second order monolayer phase transition. In addition, any combination of these effects may be responsible for the observed hysteresis. Perhaps understandably, there has been no firm quantitative model for time-dependent relaxation effects in monolayers. However, if the basic monolayer properties such as ESP, stability limit, and composition are known, a qualitative description of the dynamic surface tension, or hysteresis, may be obtained. 

Since it has been shown that nonideal mixing occurs in the 2.5-15.0 dyn cm 1 range, the excess free energies of interaction were calculated for compressions of each pure component and their mixtures to each of these surface pressures. In addition, these surface pressures are below the ESPs and/or monolayer stability limits so that dynamic processes arising from reorganization, relaxation, or film loss do not contribute significantly to the work of compression. 

Hysteresis was generally observed in the compression-expansion cycles of the force-area isotherms, indicating that the timescale for relaxation of the fully compressed film back to its expanded state was slower than the movement of the barrier of the Langmuir trough. Our studies, like many others, imply that monolayers are metastable and that reversible thermodynamics can only be applied to their analysis with caution. 

The HM-HEC monolayer at such an interface was found to strongly retard the rate of transport of small organic molecules across the interface (7). Considerable relaxation-reorientation of the HM-HEC chains slowly occurs at room temperature for as long as ten days. The desorption from the interface of HM-HEC molecules resulting from such reorientations leads to an apparently thinner and more permeable monolayer. 

Stress-Jump Experiments. The results of stress-jump experiments for HM-HEC monolayers with various compositions are shown in Table II, where the relaxation rate constants, ctRT, were calcu-... 

The segmental mobility of the polymer in the monolayer is enhanced by the solvation of the hydrophobes with toluene (9) the relaxation rate constant at the toluene/aqueous interface was three times that at the air/aqueous interface, as shown by Experiments Numbers 1 and 2 in Table II. 

The dynamic behavior of HM-HEC monolayers depends on the concentration in bulk solution (10, 11, 12) the monolayer obtained from dilute solution, having a higher relaxation rate constant, is more flexible and presumably thinner (Experiments Numbers 1 and 3). 

An increase in the amount of hydrophobic modification restricts segmental mobility by an increase of viscosity within the monolayer for the same molecular weight (300,000) and hydrophobe chain length (C g), the polymer monolayer with the higher amount of hydrophobe has a smaller relaxation rate constant (Experiments Numbers 3 and 7). 

Exp. No. Monolayer Interface Concentrat ion of Bulk Solution Degree of Compression vtl/Ao Relaxation Rate Constant aRT/A1 (sec-1) Corrected Relaxation Rate Constant aRT/AQ (sec-1)... 

Test of the Mathematical Model. In the mathematical model, behavior of the polymer monolayer was related to two parameters the degree of compression, (1-A/A ), and the ratio of the relaxation rate to the compression (expansion) rate, q. The results from three typical hysteresis experiments with three different polymers were chosen for comparison to the theory. 

Monolayer Experimental ir-A Curve Speed of Compression/cm min- Corrected Relaxation Rate Constant/ sec-3 9... 

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