Support ratio

Adsorption on solid matrices, which improves (at optimal protein/support ratios) enzyme dispersion, reduces diffusion limitations and favors substrate access to individual enzyme molecules. Immobilized lipases with excellent activity and stability were obtained by entrapping the enzymes in hydrophobic sol-gel materials [20]. Finally, in order to minimize substrate diffusion limitations and maximize enzyme dispersion, various approaches have been attempted to solubilize the biocatalysts in organic solvents. The most widespread method is the one based on the covalent linking of the amphiphilic polymer polyethylene glycol (PEG) to enzyme molecules [21]. 

We are now in a position to examine, in quantitative detail, the effect of the supporting electrolyte, at least for steady-state homovalent transport in finite planar geometry. The amount of supporting electrolyte present, relative to electroactive electrolyte, is characterized by the support ratio that was defined as... 

The value of the support ratio places an upper limit on values that can be acquired by 7, the parameter that played such an important role in Sects. 4.4 and 4.5. That this is so is evident from eqn. (97) when it is appreciated that the cathodic concentration c O) of M"+ can never be less than zero. Hence... 

From this inequality, it is possible to calculate the maximum 7 value corresponding to any given support ratio, as has been done in constructing Table 5. For large values of the support ratio, a series expansion in the form... 

Maximum 7 value calculated using eqn. (104) corresponding to a given support ratio... 

The second equality in eqn. (106) follows from eqn. (103), the definition of the support ratio. A graph showing the dependence of the limiting current on the support ratio is shown as Fig. 26. The limiting current when p = 0, the completely unsupported case, is given by... 

Fig. 26. Limiting current as a function of support ratio. Current has been normalized by division by 2z AFD1c°IL.

Thus, with a support ratio of 26 or more, the potential drop can never exceed 1 mV. It is the absence of a potential gradient to drive migration that makes diffusion dominant. 

Using this (LI) preparation procedure, Stefanovic and Walker (SO) studied the effect of stationary phase-support ratio on the gas-chromatographic separation of trifluoroacetylamino acid butyl esters using ethylene glycol adipate polyester columns. They found that, for certain amino acids, the elution pattern was a function of the amount of liquid phase on the column packing. When 0.5% ethylene glycol adipate was used, sharp well-defined peaks were obtained and all the amino acids listed in Table 6 except cysteine and methionine were completely sepa-... 

Stefanovic, M., and Walker, B. L., Effect of stationary phase-support ratio on the gas chromatographic separation of tiifluoroacetylamino acid butyl esters. Anal. Chem. 89, 710-713 (1967). 

Comparative Activity of Various Nickel, Cobalt, and Iron Catalysis Reaction temperature 200° Initial pressure 3000 p.s.i. Maximum pressure 5300-5500 p.s.i. Metal to support ratio 30 70 Catalyst volume = 15 cc. Solution volume = 15 cc. Formaldehyde concentration 12.8 mol./l. Residence period 5 4 hrs. 

It is therefore very important, in g.l.c. work of this nature, to determine retention volumes on a number of columns of different solvent/solid support ratio. This will either point to the non-existence of surface effects or the results can be used to determine a retention volume at zero mean column pressure, K r, and hence an activity coefficient, which is independent of surface effects. 

Reliable activity coefficients have been determined for benzene + polyphenyl systems by Clark and Schmidt and by Schmidt, Clark, and Gray. No surface-adsorption effect was noticed for these systems as the activity coefficients were independent of the solvent/solid support ratio. It is interesting to note that much of the work was done with the solvents in their supercooled states. The activity coefficients at 363 K range from 1.105 in the solvent biphenyl to 0.888 in w-quinquephenyl. The accuracy of their measurements, however, is limited by the accuracy of the orthodox analytical g.l.c. apparatus. 

Table 9.7. Equivalent support ratio for different excavations...

The supports mostly used for CO hydrogenation are Si02 and AI2O3, but Ti02, MgO, ZnO and other oxides are also used for on this reaction. The metal/support ratio may vary from low values up to 0.5 [2]. 

Jfj and Ki may be evaluated from plots of V lAi / " lAi) for various stationary phase/support ratios. If Ki>0 the ordinate at the origin (which gives Ki) is not zero and the slope — also positive — gives On a plot F.v/ 2 the ordinate at the origin gives and the... 

The diagrams described above, being plotted for constant concentration or amount of injected substance, allow the establishment of the tyqies of interaction exerted in the gas chromatographic system in question. Because either one or all three retention mechanisms may compensate, acquiring information about the interfacial effects necessitates the use of several stationary phase/support ratios. 

If the dilution of the solution is not infinite, K and therefore Fa become concentration dependent. Experiments employing variable stationary phase/support ratios may then be conducted in two ways (a) keeping the amount of sample constant, and modifying the concentration (b) modifying the amount of satnple and keeping concentration constant-The first method employed by Urone and Parcher [15] results in no useful information when eqn (4.7) is used becau.se there are too many variables (partition coefficients and surface/volume ratios). The second method... 

One can conclude that special care should be taken to attain infinite dilution using the minimum amount of sample sensed by the detector to keep the signal/noise ratio within acceptable limits. Martin [4] used a concentration of 0.2 (xl ( 0.002 jx mol) for each substance injected, throughout the whole range of stationary phase/support ratio (this involved using average mole fractions of solute of about 10" ), and obtained practically constant surface excesses so that Ki did not vary with dilution was indeed infinite. 

Tlie following recommendations should be tak(, n into account in order to obtain highly accurate activity coefficients from gas-liquid chromatography data (a) the adsorption at the gas-liquid interface should be avoided by measuring the retention volumes for several stationary phase/ support ratios (b) the vapour pressure of the solute should be accurately known. If these requirements are fulfilled, thou the activity coefficient at infinite dilution can be determined to an accuracy of 0.2 per cent [45] and the overall precision is higher than 0.5 per cent as compared to static measurements. 

Adsorption is absent in benzene-polyphenyl systems and activities are independent of the stationary phase/support ratio [63, 64]. At 363 K they vary from 1.105 in diphenyl to 0.888 in w -quinquephenyl. 

The coefficients of activity for solvents whether deposited or not on a support resulting from static measurements allow one to establish to what extent the support affects the values or whether differences between Yj obtained by such methods and by GLC may be ascribed to the support. Yf for n-hexane in squalane with Celite as support at 30°C is 0.649 when determined by static methods [1], while on enriched diatomite of high density it is 0.640 0.002 [57] in squalane without a support the respective values are 0.658 0.002 [7] and 0.645 [72] at the same temperature. Similar data are available for n-heptane in n-dotriacontane deposited on Celite and for the solvent in the bulk at the same temperature the values obtained are 0.695 [52] and 0.686 [73] respectively for benzene in p, S -thiodipropionitrile on Ohromosorb W the values are 3.45 [7] and 3.38 [1] respectively for cyclohexane in the same solvent deposited on the same support the values are 42.7 [7] and 40.5 [1] as obtained by chromatographic and static methods respectively. The efiEect of the support upon the activity coefficients is thus very low, in many systems being of the order of magnitude of the experimental error. For a suitable support at different stationary phase/support ratios, the error given by GLC is about 3% and in some cases it may drop to 1—2% [3]. 

Thus, in order to measure the real crystallinity it is necessary to separate the contributions to retention due to dissolution and adsorption, both above and below This may be done via the extrapolation of retention data for various stationary phase/support ratios to infinity, where the contribution of adsorption is negligible. With extrapolation in view eqn... 

B.2.1.2. Trapped Scattering traps some particles inside and at particles separatrix. These have unidirectional drifts along supports. To minimize the corresponding losses, the support ratio should be chosen well above unity. 

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