With the total number of monomers and the volume of the system fixed, a number of statistical averages can be sampled in the course of canonical ensemble averaging, like the mean squared end-to-end distance Re), gyration radius R g), bond length (/ ), and mean chain length (L). [Pg.517]

In order to get a better notion of the scaling relationship between gyration radius and average chain length for different density regimes, it is convenient [Pg.528]

Consider normal Rouse dynamics of a polymer of length A chosen such that, during its lifetime, the chain MSQ is equal to its gyration radius Rg. Within a time interval Tbreak = cf. Eq. (24), where = o exp(-7) is [Pg.546]

Let us eonsider briefly the latter for the ease of a tube. If the diameter D of the narrow tube in whieh the polymer moves is smaller than the average size (or gyration radius of the polymer eoil in bulk solution, there is a [Pg.581]

FIG. 13 (a) Log-log plot of the longitudinal part of the mean gyration radius, R, [Pg.588]

FIG. 14 (a) Plot of the normalized parallel component of the mean gyration radius i gll/i gb (open symbols), and end-to-end distance i /i gb (full symbols), vs the ratio D/i gb [19] (chain lengths N = 128, 256, 512 are distinguished by different symbols). The dashed straight line indicates the asymptotic slope of the scahng function for small D/i gb, namely —2(z/2 — (h) The same for the perpendicular components. [Pg.589]

FIG. 21 (a) Mean square gyration radius Rg vs total density C of the system for [Pg.602]

FIG. 25 (a) Variation of the mean-square gyration radius Rg with the intensity of the field (bias) and with host matrix density Cob- (b) The same for the ratio of its longitudinal and transversal components (c) The ratio between the end-to- [Pg.609]

VSTR = O Connell characteristic volume parameter, cm /g-mol ZRA = Rackett equation parameter RD = mean radius of gyration, A DM = dipole moment, D R = UNIQUAC r Q = UNIQUAC q QP = UNIQUAC q [Pg.143]

MEAN RADIUS OF GYRATION, ANGSTROMS DIPCLF MOMENT, DEBYES [Pg.232]

MEAN RADIUS OF GYRATION OF COMPONENT I I A I. CRITICAL TEMPERATURE OF COMPONENT I (DEGREES K). TEMPERATURE OF MIXTURE (DEGREES Kl. [Pg.262]

Umesi, N.O. (1980), Diffusion coefficients of dissoived gases in iiquids -Radius of gyration of solvent and solute . M.S. Thesis, The Pennsylvania State University, PA. [Pg.460]

Fig. XI-6. Polymer segment volume fraction profiles for N = 10, = 0-5, and Xi = 1, on a semilogarithinic plot against distance from the surface scaled on the polymer radius of gyration showing contributions from loops and tails. The inset shows the overall profile on a linear scale, from Ref. 65. |

For free particles, the mean square radius of gyration is essentially the thennal wavelength to within a numerical factor, and for a ID hamionic oscillator in the P ca limit. [Pg.458]

The radius of gyration of tire whole particle, R can be obtained from the distance distribution fimction p(r) as [Pg.1400]

The above radius of gyration is for an isotropic system. If the system is anisotropic, the mean square radius of gyration is equal to [Pg.1414]

Figure C2.5.6. Thennodynamic functions computed for the sequence whose native state is shown in figure C2.5.7. (a) Specific heat (dotted curve) and derivative of the radius of gyration with respect to temperature dR /dT (broken curve) as a function of temperature. The collapse temperature Tg is detennined from the peak of and found to be 0.83. Tf, is very close to the temperature at which d (R )/d T becomes maximum (0.86). This illustrates |

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