Second virial coefficient estimated

Selected entries from Methods in Enzymology [vol, page(s)] Association constant determination, 259, 444-445 buoyant mass determination, 259, 432-433, 438, 441, 443, 444 cell handling, 259, 436-437 centerpiece selection, 259, 433-434, 436 centrifuge operation, 259, 437-438 concentration distribution, 259, 431 equilibration time, estimation, 259, 438-439 molecular weight calculation, 259, 431-432, 444 nonlinear least-squares analysis of primary data, 259, 449-451 oligomerization state of proteins [determination, 259, 439-441, 443 heterogeneous association, 259, 447-448 reversibility of association, 259, 445-447] optical systems, 259, 434-435 protein denaturants, 259, 439-440 retroviral protease, analysis, 241, 123-124 sample preparation, 259, 435-436 second virial coefficient [determination, 259, 443, 448-449 nonideality contribution, 259, 448-449] sensitivity, 259, 427 stoichiometry of reaction, determination, 259, 444-445 terms and symbols, 259, 429-431 thermodynamic parameter determination, 259, 427, 443-444, 449-451. 

The unconventional applications of SEC usually produce estimated values of various characteristics, which are valuable for further analyses. These embrace assessment of theta conditions for given polymer (mixed solvent-eluent composition and temperature Section 16.2.2), second virial coefficients A2 [109], coefficients of preferential solvation of macromolecules in mixed solvents (eluents) [40], as well as estimation of pore size distribution within porous bodies (inverse SEC) [136-140] and rates of diffusion of macromolecules within porous bodies. Some semiquantitative information on polymer samples can be obtained from the SEC results indirectly, for example, the assessment of the polymer stereoregularity from the stability of macromolecular aggregates (PVC [140]), of the segment lengths in polymer crystallites after their controlled partial degradation [141], and of the enthalpic interactions between unlike polymers in solution (in eluent) [142], as well as between polymer and column packing [123,143]. 

Another important application of experimentally determined values of the osmotic second virial coefficient is in the estimation of the corresponding values of the Flory-Huggins interaction parameters x 12, X14 and X24. In practice, these parameters are commonly used within the framework of the Flory-Huggins lattice model approach to the thermodynamic description of solutions of polymer + solvent or polymer] + polymer2 + solvent (Flory, 1942 Huggins, 1942 Tanford, 1961 Zeman and Patterson, 1972 Hsu and Prausnitz, 1974 Johansson et al., 2000) ... 

Use these data to estimate 9 and k for this system. Does AS agree with the expected entropy contribution to the second virial coefficient ... 

Here BLS is the second virial coefficient of the polymeric solute in the original solution before ultracentrifugation. BLs is a quantity which can be obtained in light-scattering experiments (17, 25, 30) or in Archibald experiments (31), provided it is calculated from a plot of l/MWapp° vs. c. Here 1/Mw pp° is obtained from values of Mw pp (at rm or rb) that have been extrapolated to zero time. The reason for using Equation 75 is that it leads to a simple method of estimating the MWD in nonideal solutions. 

To have an idea about the range of the repulsion required to provide such a high virial coefficient, it should be noted that, if the hard-core repulsion, infinite in magnitude, is extended with 15 A (above the 2a separation), 2 increases from 4 to only 5.6. If the range of the hard-core repulsion is extended with 30 A, 2 increases to 7.55, while 60 A leads to 12.8. From these simple estimations one can infer that the repulsion needed to explain the measured second virial coefficient for apoferritin molecules should have a much longer range than that typically observed for the traditional hydration force. 

Fig. 36a and b. Second virial coefficient A2 of a) cellulose nitrate (CN) (Nc = 13.9%) and b) CN (Nc = 12.9%), in acetone78 79> O experimental data 2). Lines are calculated by using the penetration function j/ from short and long range interaction parameters A and B, which are estimated by methods 2C (full line), 2D (broken line), 2E (dotted line), and 2G (chain line), together with experimental [Pg.41]

How efficient is the described representation of the ArCC>2 potential To answer this question the above PES along with a few empirical potentials have been used to derive a number of properties, such as the ground vibrational state and dissociation energy of the complex, ground state rotational constants, the mean square torque, the interaction second virial coefficients, diffusion coefficients, mixture viscosities, thermal conductivities, the NMR relaxation cross sections, and many others [47]. Overall, the ab initio surface provided very good simulations of the empirical estimates of all studied properties. The only parameters that were not accurately reproduced were the interaction second virial coefficients. It is important that its performance proved comparable to the best empirical surface 3A of Bohac, Marshall and Miller [48], This fact must be greeted with satisfaction since no empirical adjustments were performed for the ab initio surface. 

The virial coefficients reflect interactions between polymer solute molecules because such a solute excludes other molecules from the space that it pervades. The excluded volume of a hypothetical rigid spherical solute is easily calculated, since the closest distance that the center of one sphere can approach the center of another is twice the radius of the sphere. Estimation of the excluded volume of llexible polymeric coils is a much more formidable task, but it has been shown that it is directly proportional to the second virial coefficient, at given solute molecular weight. 

Estimate Z, and at 300 K and 6 bar for propane given the following values of the second virial coefficient for propane. 

The measured volumetric flow rate of ethane at 10.0 atm absolute and 35 C is 1.00 x 10 L/h. Using an estimated value of the second virial coefficient in the truncated virial equation (Equation 5.3-4), (a) calculate V (L/mol) (b) estimate the compressibility factor,and (c) determine the mass flow rate of ethane in kg/h. 

However, Eq. (3.37) is more convenient in application and is at least as accurate as Eq. (3.38). Thus when the virial equation is tmncated to two terms, Eq. (3.37) is preferred. This equation satisfactorily represents the P K T behavior of many vapors at subcritical temperatures up to a pressure of about 5 bar. At higher temperatures it is appropriate for gases over an increasing pressure range as the temperature increases. The second virial coefficient B is substance dependent and a function of temperature. Experimental values are available for a number of gases, Moreover, estimation of second virial coefficients is possible where no data are available, as discussed in Sec. 3.6. 

A system formed of methane( 1) and a hght oil(2) at 200 K and 30 bar consists of a vapor plrase containing 95 mol-% methane and a hquid phase containing oil and dissolved metlrane. The fugacity of the methane is given by Henry s law, and at the temperature of interest Henry s constant is Hi = 200 bar. Stating any assumptions, estimate the equilibrium mole fraction of methane in the liquid phase. The second virial coefficient of pure metlrane at 200 K is —105 cm mol . ... 

These data were obtained by estimating the chain expansion factor a from viscosity and osmotic second virial coefficient measurements, through the combined use of equations (10) and (11). These results tend to confirm the main predictions of the theory presented by the above mentioned authors both as regards the steep decrease in with... 

Measurement of the temperature dependence of second virial coefficient A2 for polymers with known molar mass M and Kuhn length b allows estimation of the number of thermal blobs per chain A /gj using Eq. (3.109). 

Compare the thermophysical quantities such as, for example, the second virial coefficients, and estimate deviations. 

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