Function of time

The first requirement is a source of infrared radiation that emits all frequencies of the spectral range being studied. This polychromatic beam is analyzed by a monochromator, formerly a system of prisms, today diffraction gratings. The movement of the monochromator causes the spectrum from the source to scan across an exit slit onto the detector. This kind of spectrometer in which the range of wavelengths is swept as a function of time and monochromator movement is called the dispersive type. 

The paper discusses the application of dynamic indentation method and apparatus for the evaluation of viscoelastic properties of polymeric materials. The three-element model of viscoelastic material has been used to calculate the rigidity and the viscosity. Using a measurements of the indentation as a function of a current velocity change on impact with the material under test, the contact force and the displacement diagrams as a function of time are plotted. Experimental results of the testing of polyvinyl chloride cable coating by dynamic indentation method and data of the static tensile test are presented. 

Figure 2 Fluorescence and Extinction of a MP Suspension as a Function of Time...

Case 2. The surface potential is measured as a function of time. Here, since by Eq. IV-19 AV = 4im/I/c, then... 

Fig. XI-2. Variation of physically adsorbed (Pp) and chemically adsorbed (Pc) segments as a function of time for cyclic polymethylsiloxane adsorbing from CCI4 onto alumina (from Ref. 43). Note that the initial physisoiption is overcome by chemical adsorption as the final state is reached. [T. Cosgrove, C. A. Prestidge, and B. Vincent, J. Chem. Soc. Faraday Trans., 86(9), 1377-1382 (1990). Reproduced by permission of The Royal Society of Chemistry.]...

The preceding treatment relates primarily to flocculation rates, while the irreversible aging of emulsions involves the coalescence of droplets, the prelude to which is the thinning of the liquid film separating the droplets. Similar theories were developed by Spielman [54] and by Honig and co-workers [55], which added hydrodynamic considerations to basic DLVO theory. A successful experimental test of these equations was made by Bernstein and co-workers [56] (see also Ref. 57). Coalescence leads eventually to separation of bulk oil phase, and a practical measure of emulsion stability is the rate of increase of the volume of this phase, V, as a function of time. A useful equation is... 

LID) see Ref. 139. In this last method, a small area, about 0.03 cm radius, is depleted by a laser beam, and the number of adatoms, N(t), that have diffused back is found as a function of time. From Pick s second law of diffusion ... 

Figure B3.4.8. The correlation fimction c(t) = (ii1q vii(0) as a function of time for photodissociation m a collinear (or tliree-dimensional) polyatomic case. There are tliree relevant time scales T, which measures how rapidly the initial wavefimction dephases T2, which measures how long it takes this mitial wavefimction to regroup and which measures how long the wavefimction takes to Teak to other degrees of freedom. In practice, photodissociation experiments may yield spectra which are more blurred, and/or are not...

Figure B3.4.15. A possible Feymnaim path trajectory for a ID variable as a function of time. This trajectory carries an oscillating component with it, where. S is the action of the trajectory. The trajectory is highly fluctuating its values at each time step (v(dt), etc) are not correlated.

Figure Cl.5.8. Spectral jumping of a single molecule of terrylene in polyethylene at 1.5 K. The upper trace displays fluorescence excitation spectra of tire same single molecule taken over two different 20 s time intervals, showing tire same molecule absorbing at two distinctly different frequencies. The lower panel plots tire peak frequency in tire fluorescence excitation spectmm as a function of time over a 40 min trajectory. The molecule undergoes discrete jumps among four (briefly five) different resonant frequencies during tliis time period. Arrows represent scans during which tire molecule had jumped entirely outside tire 10 GHz scan window. Adapted from...

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

Figure C2.18.7. The integrated absorbance of tire Si-Cl stretching vibration at 625 cm and tire SiO-H stretching vibration at 3740 cm as a function of time during tire (A) SiCl and (B) H2O half-reactions at 600 K and 10 Torr. Reproduced from [95].

The description of chemical reactions as trajectories in phase space requires that the concentrations of all chemical species be measured as a function of time, something that is rarely done in reaction kinetics studies. In addition, the underlying set of reaction intennediates is often unknown and the number of these may be very large. Usually, experimental data on the time variation of the concentration of a single chemical species or a small number of species are collected. (Some experiments focus on the simultaneous measurement of the concentrations of many chemical species and correlations in such data can be used to deduce the chemical mechanism [7].)... 

Section IB presents results that the analytic properties of the wave function as a function of time t imply and summarizes previous publications of the authors and of their collaborators [29-38]. While the earlier quote from Wigner has prepared us to expect some general insight from the analytic behavior of the wave function, the equations in this secbon yield the specific result that, due to the analytic properties of the logarithm of wave function amplitudes, certain forms of phase changes lead immediately to the logical necessity of enlarging... 

Figure 7. Alpha Mulliken population on Li(2) as functions of time for different initial conditions.

Molecular clynainics sim illations calculate future position s and velocities of atoms, based on their current positions and velocities. A sim Illation first determ in es the force on each atom (lY) as a function of time, ct ual to the negative gradient of the polen tial en ergy (ct]uation 2 I ),... 

Two different types of dynamic test have been devised to exploit this possibility. The first and more easily interpretable, used by Gibilaro et al [62] and by Dogu and Smith [63], employs a cell geometrically similar to the Wicke-Kallenbach apparatus, with a flow of carrier gas past each face of the porous septum. A sharp pulse of tracer is injected into the carrier stream on one side, and the response of the gas stream composition on the other side is then monitored as a function of time. Interpretation is based on the first two moments of the measured response curve, and Gibilaro et al refer explicitly to a model of the medium with a blmodal pore... 

If F is the operator for momentum in the x-direction andA (x,t) is the wave function for x as a function of time t, then the above expansion corresponds to a Fourier transform o/ P... 

Molecular dynamics is essentially a study of the evolution in time of energetic and structural molecular data. The data is often best represented as a graph of a molecular quantity as a function of time. The values to be plotted can be any quantity x that is being averaged over the trajectory, or the standard deviation, Dx. You can create as many as four simultaneous graphs at once. 

Construct a graph of pH as a function of time, and suggest an appropriate sampling frequency for a long-term monitoring program. 

The change in current as a function of time in controlled-potential coulometry is approximated by an exponential decay thus, the current at time t is... 

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