Flory exponent

M. Jaric, G. F. Toothill. Thermodynamic polydispersity and the Flory exponent. Phys Rev Lett 55 2891-2894, 1985. 

In Fig. 21(a) we plot the variation of R with increasing system density Cobs 3.nd, for comparison, also give the respective change for a system of moving medium (dynamic host matrix) of equal density. This result is in good agreement with recent predictions [89]. If one defines an effective Flory exponent from the scaling relation Rg oc it is then evident from... 

The final rule follows from the transformational invariance of the mean squared end-to-end distance [Pg.73]

As pointed out in [6] the extended coil conformation in good solvents leads to different exponents for p=air N p, and Tp=a ri N tyik Tand D=a k T/ (rfN ) with the Flory exponent v and the numerical prefactors aj also dependent on the conformation. 

Flory exponent for the polymer chain size Flory radius... 

Here F(q) is a function of radius of gyration and composition of the block copolymer. This equation should be compared with eqn 2.11 for block copolymer melts. The effective chi parameter in semidilute solution is X N = %abiV0(1+ )/(,v l), where yAB is the chi parameter for the block copolymer, v is the Flory exponent (v = 0.588 in good solvents) and z = 0.22 (Fredrickson and Leibler 1989 Olvera de la Cruz 1989). The function F q) has a minimum, and hence S(<7)-1 has a maximum, at q = q, which is independent of % and thus temperature. Empirically, is found to be inversely proportional to temperature... 

As shown in Figure 27c, the rotational relaxation time varies as a power of length, zr N with /u = 2.6 0.4. The experimental result is in remarkable agreement with the scaling behavior of the rotational relaxation zr°c A/1 l2v with theory = 2.5, which follows from the Rouse model and the Flory exponent v = 3/4.189... 

Flory exponent and is the arm degree of polymerization. The concentration profile scales with the radial distance r as rc, whereas... 

In Euclidean cZ-dimensional spaces Flory exponent depends only on d. A good (although not exact) estimation was given by Flory formula, Eq. (9) [7, 8], It is well known [47] that the critical phenomena depend by the decisive mode on various ftactal characteristics of basic stmcture. It becomes obvious, that excepting the ftactal (Hausdorflf) dimension Dj. physical phenomena on ft actals depend on many other dimensions, including skeleton fractal dimension [48], dimension of minimum (or chemical) distance [29] and so on. It also becomes clear, that regular random walks on fractals have anomalous fractal dimension [49] and that the vibrational excitations spectrum is characterized by spectral (fiac-ton) dimension d=2D d [41, 50],... 

The authors [51] criticized the Eq. (20), since they proved, that if SAW moved over fractal skeleton (otherwise it will be captured by handling or dead ends, that is important particularly for branched polymer chains), then Flory exponent should depend on the skeleton properties only, but not on Let us remind, that the skeleton notion is defined as follows [48]. The two cluster end points and are considered, which are divided by the distance, comparable with the correlation length of system. 

Isaacson, J. Lubensky, T. C. Flory exponents for generalized polymer problems. J. Phys. Lett. (Paris), 1980, 41(19), L469-L471. 

It should be noted, that the considered above correction can be obtained and without fractal analysis application as well, using well-known Flory concept, that follows from the Eq. (1) of Chapter 1. However, obtaining of the anal dical correlation between Flory exponent and structural characteristics of polymers in solid phase is very difficult, if possible at all. At the same time this can be made within the framework of fractal analysis, since both macromolecular coil [25] and solid-phase polymer structure [62] are fractal objects. Hence, the possibility of solid-phase polymers properties quantitative prediction appears in such sequence molecular characteristics (for example, ) structure of macromolecular coil in solution polymer condensed state structure— polymer properties. In Section 2.6, this problem will be considered in detail. These considerations predetermined the choice of fractal analysis in Ref. [59] as a mathematical calculus. 

Flory exponent for the coronal bloek A (v 3/5 and v = 1/2 under good and theta-... 

Translational entropy of micelles Dead time of mixing Flory exponent Volume of component i Sample volume in cm ... 

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