Adsorption isotherm standard deviation

The mobile phase was water in which the moderator alcohols were dissolved. It is seen that the linear relationship is completely validated and the data can provide the adsorption isotherms in the manner discussed. The mean surface area was found to be 199 m /g with a standard deviation between the different alcohols of 11 m /g. 

The standard deviation has been determined as ct = j where v is the number of degrees of freedom in the fit. The parameters for the molecular interaction /3, the maximum adsorption Too, the equilibrium constant for adsorption of surfactant ions Ki, and the equilibrium constant for adsorption of counterions K2, are thus obtained. The non-linear equations for the Frumkin adsorption isotherm have been numerically solved by the bisection method. 

The equilibrium isotherms depend on the parameters that characterize the physical state of the system and the chemical potential of the compounds studied in this system selected, i.e., its temperature and pressure, the chemical compositions of the mobile and the solid phases. The last of these parameters is far more difficult to investigate than that of the other three. Suffice it to say that important variations of the isotherm parameters have been observed for different brands of Cig-bonded silica. However, the best isotherm model accormting for the adsorption data measured on these different brands remained the same [61] while the colmnn to column reproducibility of the data was excellent for at least one brand and probably for several others [11,121,122], with relative standard deviations for the parameters being of the order of a few percent [123]. 

FIGURE 19.7. Interfacial activity in a Type I blend of an A-B diblock copolymer added to a blend of A and B homopolymers [A = SPB(89) and B = SPB(63)]. A/a = 4,230 and A/b = 3,600 for the homopolymers, while A/Ab = 790 and Nsb = 730 for the block copolymer. Symbols show experimental measurements using secondary-ion mass spectrometry (SIMS), and curves show SCFT predictions using x and / values from Tables 19.1 and 19.2. (a) Volume fraction profile in loglinear format of the diblock copolymer for a sample with 0.07 volume% block copolymer with an A/B interface at z = 190 nm. (b) Volume fraction profile in linear-linear format of the diblock copolymer for a sample with 0.07 volume% block copolymer with an A/B interface at z = 190 nm. The cross-hatched area represents the adsorbed amount, F. (c) Adsorption isotherm the dependence of the adsorbed amount, r, on the copolymer volume fraction in the A-rich phase ab/a- (d) The thickness of the adsorbed layer (standard deviation of the volume fraction profile near the peak), a, plotted versus the amount adsorbed, F. 

The physisorption isotherm on a mesoporous or macroporous adsorbent follows the same monolayer-multilayer path as on the corresponding non-porous surface until the secondary process of capillary condensation occurs. In the case of a macro-porous solid, the deviation from the standard monolayer-multilayer isotherm does not take place until very high relative pressures are attained (with nitrogen adsorption at 77 K, this would be at p)p° > 0.99). 

---