Calculations for sucrose

The CALCULATION function provides a variety of routine calculations performed in most ultracentrifugation laboratories. Included are dilution calculations for sucrose, a pelleting time calculation, and a calculation for determining rotor speed reductions for salt gradients. As with the INFORMATION function, the CALCULATION function is a support tool in the effort to efficiently design and carry out a separation. 

Very few calculations of adiabatic energy maps for disaccharides coupled with molecular dynamics simulations have been undertaken, partially as a result of the great expense and labor involved in such studies. One molecule which has been studied by both of these t3npes of molecular mechanics calculations is sucrose. 

Figure 2. The calculated adiabatic energy map for sucrose. Contours are indicated at 2, 4, 6, and 8 kcal/mol above the global SI minimum. The stars refer to the various minima calculated with the present potential energy function.

The ciystal habit of sucrose and adipic add crystals were calculated from their intern structure and from the attachment energies of the various crystal faces. As a first attempt to indude the role of the solvent on the crystal habit, the solvent accessible areas of the faces of sucrose and adipic add and were calculated for spherical solvent probes of difierent sizes. In the sucrose system the results show that this type of calculation can qualitatively account for differences in solvent (water) adsorption hence fast growing and slow growing faces. In the adipic add system results show the presence of solvent sized receptacles that might enhance solvent interadions on various fares. The quantitative use of this type of data in crystal shape calculations could prove to be a reasonable method for incorporation of solvent effeds on calculated crystal shapes. 

Examples of the results of this type of calculation are shown for sucrose (2) and terephthalic acid (2) in Figures 1 and 2. 

Thomsen,133 Smolenski and Kozlowski,134 and Reeves and Blouin131 observed that sodium hydroxide has a relatively large effect on the optical rotation of sucrose. a,a-TrehaloSe,m on the other hand, is affected only slightly. Thomsen133 and Reeves and Blouin131 made no attempt to interpret the unusual behavior of sucrose Smolenski and Kozlowski,134 however, assumed that the reaction was that of alcoholate formation, and they calculated dissociation constants for sucrose. 

Ionization constants have been determined for numerous simple carbohydrates (10,13, i5, 25, 45), as well as for cellulose (32, 43), wheat starch (43), and alginate (43). Selected carbohydrates with their corresponding pK values are presented in Table I. The analytical methods involved in these determinations include conductimetry, potentiometric titration, thermometric titration, and polarimetry. Polarimetry was used by Smolenski and co-workers (45) to calculate a first and a second ionization constant for sucrose at 18°C (Ki = 3X 10"13 K2 = 3 X 10"14). 

Measure the volumes of sucrose solution and water consumed. Calculate the preference for the sucrose solution as a percentage of total liquid consumed and total sucrose intake in mg/g body weight. In addition, commercially available automated lick-counters (lickometers) may be used (e.g., by Lafayette Instrument Co, Lafayette IN, United States or Columbus Instruments, Columbus OH, United States). Assess the number of licks at each bottle for the duration of the test (i.e., 24-72 h) per 100 mg of body weight, and the preference for sucrose as a percentage of total licks (23, 27, 28) (see Notes 4-6). 

Figure 93. Comparison of Observed and Calculated Rates of Flow for Sucrose Solutions in Consistometer.

For B = A, the tracer diffusion coefficient equals the self-diffusion coefficient, D lba= Dla- 1° Table 6-6 the self-diffusion coefficient of water and some diffusion coefficients of organic solutes in water at infinite dilution calculated with Eq. (6-31) are compared with experimental values (Reid et al., 1987). The experimental value for sucrose is from Cussler (1997). 

K. Determine the molecular weight of sucrose from these data, and discuss the reason for any discrepancies compared to the molecular weight as calculated from the formula for sucrose. 

Figure 6 Schematic of the temperature dependence of configurational entropy definition of fictive temperature. Data calculated using input data for sucrose (see text).

Calculated using Gordon-Taylor equation with an intrinsic glass transition, 7 of 74°C (347 K) and - 139°C (135 K) for sucrose and water, respectively, and a Gordon-Taylor constant value of 0.13675. 

The composition of the mixture influences the glass-transition phenomenon in a similar way. Figure 21.4 shows the glass-transition curves calculated for aqueous solutions of MOR-REX 1910 and sucrose. The proportion of sucrose was 5, 10, and 15% with respect to the solids content. The curves show the decrease in Tg with an increase in sucrose concentration, a behavior... 

Phase equilibria in water have been described by Kelly, who studied the effect of hexoses, sucrose, and inorganic salts on each other. The conclusion was reached that, for sucrose, the solubility of the second solute influences the composition at the invariant point, but for D-fructose, this effect is zero because of the high solubility of this sugar in water. Viscosity and density have also been evaluated at different temperatmes in methyl sulfoxide, and were fitted to appropriate equations by use of least-squares methods. The apparent molal volume calculated in this way is in perfect agreement with the theoretical data, whereas the differences for D-glucose and sucrose are 8 and 4%, respectively. 

Figure 13.14 Differences in equilibrium melting temperature for ice crystals based on Ostwald ripening calculations for an ice-sucrose solution. (From Hartel 1998a with permission.)...

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