Florys formula

Equation 5 corrects the expression given by Beer et al. [43] by a factor Pk/b2. It is equivalently written in the form of the modified Flory formula [1], as... 

This is the so-called ideal value on the Bethe lattice, which, when ps = 1, recovers the Flory formula. 

Equation 2.44 is the well-known Flory formula which is widely used in the study of liquid crystalline polymers. It should be pointed out that cj> is only the minimal solution of Equation 2.41 at which the partition function first shows a maximum. At this volume fraction cf>, Zmax is actually less than the Z at the disordered state (y = x). The system is at a meta-stable state only when the volume fraction further increases to a greater value in which the system is indeed at a stable state. 

Baranov and co-workers [51] introduced the dimension dp, determined from the Flory formula [53] for good solvents ... 

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],... 

Euclidean dimension Flory formula lattice animals Monte-Carlo method phantom fractal true self-avoiding walk... 

A surprisingly good approximation for the critical exponent 1/ of SAW in genersJ dimension d is given by the Flory formula [10] ... 

Let us turn our attention to the scaling of a SAW on a disordered lattice with strong disorder, directly at p = ppc- The Flory formula (2), giving a surprisingly good estimation for the critical exponent i/ of SAWs on pure lattice, has tempted a number of authors to search for generalizations to determine the exponent i/p of SAWs on the percolation cluster [16]. The most direct one is ... 

Hammal et al. [31] suggested that C = 1> which leads to the Flory formula ... 

In the preceding sections we studied the properties of SAWs on several different fractals. For the calculation of critical exponents of SAWs on still other fractals, see for example [25]. It would appear that for each fractal, one has to write down the polynomial recursion equations, and calculate the values of critical exponents using the technique outlined. There is no simple expresion for the critical exponents as a function of the geometrical properties of the fractal, ( an improved Flory formula ) that would allow one to predict these without doing the full calculation. Unfortunately, this level of understanding of the problem is still not achieved. 

This has also been studied experimentally and theoretically by the Saclay group.Let us start from the good solvent side, at a fixed concentration c = and progressively reduce the excluded volume parameter i = a (1 - 2 )- When u a (athermal solvent), the scaling formulas of Chapter III hold. When v becomes much smaller than a , the single chain radius/ decreases and the overlap concentration c = N/R increases. To make this more precise, we use the Flory formula for / as a function of v [eq. (1.38)]... 

In the original formula of Flory, a = 2.6(3/27t). Stockmayer suggested that the choice of a = 4/3(3/2ti) gives the exact result of first order perturbation theory near 6 temperature and the result of equation (23) in good solutions. With this choice of a, equation (24) is called the modified Flory formula which can be derived in a systematic way. Many approximate closed expressions for a exist in the literature which are adequately reviewed. ... 

N Concentration of irregular polymers from C-NMR Np Concentration of randomly occurring polymers along the chain/Flory formula K polymers are insoluable in isooctane, D polymers are soluble in isooctane. Reproduced with permission from N. Uryu and K. Alyiiruk, Journal of Polymer Science Part A Polymer Chemistry, 1989, 27, S, 1749. 1989, Wiley. [113] ... 

---