Mass radius method

In Eq. 1.2, U, V, Po., i, f, and R are the amplitude of the voltage pulse, the particle volume, electrolyte resistivity, aperture current, particle shape factor, and aperture radius, respectively. If a constant particle density is assumed, the pulse height is proportional to the particle mass. The measured particle size can be channelyzed using the pulse height analyzer circuit, and a particle size distribution is thus obtained. The electrical response of the instrument is essentially independent of shape for particles of the same voliune, both in theory and in practice. A typical measurement takes less than a minute, as counting and sizing rates of up to 10,000 particles per second are possible. The accuracy of size measurements is usually within 1-2%. Calibration can be performed using known size standards or by the mass balance method [15]. 

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

Both Reynolds and Karim worked at neutral pH, with denatured proteins, and with reduced disulfide bonds. Under these conditions, proteins are in a random coil conformation (Mattice et al., 1976), so that their hydrodynamic radius is monotoni-cally related to their molar mass. Takagi et al. (1975) reported that the binding isotherm of SDS to proteins strongly depends upon the method of denaturing disulfide bonds. Presumably, protein-SDS complexes are not fully unfolded when disulfide bonds are left intact, which breaks the relationship between molar mass and hydrodynamic... 

Because the rotating motion of the gas in the cyclone separator arises from its tangential entry and no additional energy is imparted within the separator body, a free vortex is established. The energy per unit mass of gas is then independent of its radius of rotation and the velocity distribution in the gas may be calculated approximately by methods discussed in Volume 1, Chapter 2. 

The architecture of hypeibranched polymers and dendrimers is connected with difficulties in determining molar mass. Many of the common characterization techniques—e.g. size exclusion chromatography (SEC)—used for polymers are relative methods where polymer standards of known molar mass and dispersity are needed for calibration. Highly branched polymers exhibit a different relationship between molar mass and hydrodynamic radius than their linear counterparts. 

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