Pendular states

Kim W and Felker P M 1996 Spectroscopy of pendular states in optical-field-aligned species J. Chem. Phys. 104 1147-50... 

In the pendular state, shown in Figure la, particles ate held together by discrete lens-shaped rings at the points of contact or near-contact. For two uniformly sized spherical particles, the adhesive force in the pendular state for a wetting Hquid (contact angle zero degree) can be calculated (19,23) and substituted for H. in equation 1 to yield the foUowing, where y is the Hquid surface tension in N/m. 

It is evident, by comparing equations 2 and 3, that tensile strength in the pendular state is about one-tbhd that in the capillary state. Intermediate Hquid contents in the funicular state (Fig. lb) yield intermediate values that can be approximated as foUows ... 

Pendular state is that state of a liquid in a porous solid when a continuous film of liquid no longer exists around and between discrete particles so that flow by capillary cannot occur. This state succeeds the Funicular state. 

FIG. 20-64 Three states of liquid content for an assembly of spherical particles. (a) Pendular state, (h) Funicular state, (c) Capillary state. [Newitt and Con-way-Jones, Trans. Inst. Chem. Eng. (London), 36, 422 (1958).]... 

The spherical pendulum, which may be used to model the bending states of HCP [7] and the pendular states of dipolar molecules in strong electric fields [8], is of... 

The tensile strength of the agglomerate in the pendular state is readily obtained by combining Eqs. (4) and (12) ... 

In other words, the pellets in the capillary regime are about three times stronger than those in the pendular state. 

Pendular state Superpositions of field-free rotational eigenstates in which the molecular axis librates about the field direction. Pendular states are eigenstates of the rotational Hamiltonian plus the dipole potential. 

The experiments described above used nanosecond laser pulses, which are much longer than the rotational period of the molecules. At the termination of the pulse, the pendular state that is formed relaxes adiabatically to a free-rotor eigenstate. If instead picosecond laser pulses are used, a rotational wave packet is formed by successive absorption and re-emission of photons during the laser pulse. Such wave packets are expected to display periodic recurrences of the alignment after the end of the pulse. 

Figure 2-3. An illustration of how well molecules can be oriented in electric fields of moderate strength. The wavefunction shown in the figure is for the = 0 pendular state for N2-HF at 16.6 kV cm 1.

Figure 2-8. A pendular state (M = 0) photofragment C02-HF angular distribution corresponding to detection of the C02 fragment, showing at least three important dissociation channels. The expansion factor for the second trace is five.

In the pendular state, the particles have been exposed to sufficient granulating solution for liquid bridges to begin to form. Since the pendular state is characterized by a... 

Friedrich, B. and Herschbach, D.R. (1991). Spatial orientation of molecules in strong electric fields and evidence for pendular states, Nature (London), 353, 412-414. 

As the liquid continues decreasing we revert to the pendular state. This state is perfectly reversible for increasing or decreasing moisture conditions and, as before, is 4.1 a/r. This value is the one obtained when the water wedge is the maximum which can be maintained. If we consider Eq (15-1), we see that as 6 decreases R and R2 become equal, and P approaches infinity. Thus, the pendular stage during the decreasing... 

At low liquid levels, discrete lens-shaped rings are formed at the points of contact of the particles (Fig. 2.4). This is the pendular state of liquid content which persists until the liquid rings begin to coalesce. For uniform spheres, this occurs when ... 

Fig. 2.3. Mobile liquid bonding states of liquid content in an agglomerate. (A) pendular state (B) funicular state (C) capillary state (D) particles in liquid droplet.

In the pendular state, bonding is localized at the points of particle contact and calculated values of the cohesive force between two particles may be substituted directly for H into eqn. (4) to yield the tensile strength of the assembly. For two particles in contact, H is given by [8,10] ... 

Comparing eqn. (10) and eqn. (13), tensile strength in the pendular state is about of that in the capillary state, while the funicular state yields intermediate values. As shown in Fig. 2.6, tensile strength in the funicular state can be approximated by ... 

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