Volume relationship with number

Several papers compare the properties of sulfobetaine (meth)acrylic polymers. NMR spectra and solution properties of 23a and 23b [59,60] are correlated with data from the corresponding polycarbobetaines [26]. The photophysical and solution properties of pyrene-labeled 23c were studied in terms of fluorescence emission. Addition of surfactants induces the formation of mixed micelles in aqueous solution [61]. Excluded volume effects of the unlabeled polymer were measured by light scattering [62], its adsorption on silica was studied by adsorbance measurement and ellipsometry [62,63], and the electrostimulated shift of the precipitation temperature was followed at various electric held intensities [64]. Polysulfobetaines may accelerate interionic reactions, e.g., oxidation of ferrocyanide by persulfate [65]. The thermal and dielectric properties of polysulfobetaines 23d were investigated. The flexible lateral chain of the polymers decreased Tg, for which a linear relationship with the number of C atoms was shown [66,67]. 

Figure 88A shows a plot of the JC analyses for LCB level as a function of the catalyst pore volume. The LCB levels indicate a single relationship with pore volume, although high and low surface areas are well distributed over the whole graph. In Figure 88B, the LCB level is shown as a function of the average coordination number of the silica, as defined in Scheme 21. Plotting the data in this way produces a straight line, making it even clearer that LCB levels respond to the strength of the silica matrix. MW (not shown) was also entirely a function of pore volume in this series [500].

This simply shows that there is a physical relationship between different quantities that one can measure in a gas system, so that gas pressure can be expressed as a function of gas volume, temperature and number of moles, n. In general, some relationships come from the specific properties of a material and some follow from physical laws that are independent of the material (such as the laws of thermodynamics). There are two different kinds of thermodynamic variables intensive variables (those that do not depend on the size and amount of the system, like temperature, pressure, density, electrostatic potential, electric field, magnetic field and molar properties) and extensive variables (those that scale linearly with the size and amount of the system, like mass, volume, number of molecules, internal energy, enthalpy and entropy). Extensive variables are additive whereas intensive variables are not. 

This may be based on product sold by weight, volume, or number. Container capacity is a critical feature bearing relationships with product filling speed, the declared contents and headspace (vacuity or ullage). The ullage (airspace above product) must be adequate to allow for the thermal expansion of the product. This is particularly important with alcohol-based products in narrow necked containers. The capacity usually relates to either a brimful capacity or a defined fill point. 

In the further analysis, let us consider a porous body with length I2. Furthermore, let us examine the resistance factor buildup vs injected pore volumes relationship for an li and I2 — h section, where hinjection time, the number of the injected pore volumes in the 0—/j section is (/j — li)/li times the injected pore volumes in the I2 — I1 section. If li<(l2 — li) the li/(l2 — h) ratio would show how many times lower the slope of the resistance factor versus injected pore volumes relationship is in the O-ij segment. This is true provided that the rate of polymer buildup as a function of time is the same at any location. But it was earlier pointed out that the rate of polymer buildup as a function of time is the highest at the inlet face. Consequently, there should be an /j location, when for the 0—/j distance the slope of Rp vs PVI is equal to the slope for I2 — li distance. 

Electrical conductivity in technical silicate glasses is, in general, a result of the migration of ions - mostly alkali ions. At room temperature, the mobility of these ions is usually so small that the volume resistivity, with values above 10 2 cm, is beyond the range of measurement. The ion mobility increases with increasing temperature. Besides the number and nature of the charge carriers, the structural effects of other components also influence the volume resistivity and its relationship to temperature. The Rasch and Hinrichsen law applies to this relationship at temperatures below the transformation range ... 

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