Statistical segments

Helfand and Tagami [75,76] introduced a model which considered the probability that a chain of polymer 1 has diffused a given distance into polymer 2 when the interactions are characterised by the Flory-Huggins interaction parameter x They predicted that at equilibrium the thickness , d c, of the interface would depend upon the interaction parameter and the mean statistical segment length, b, as follows ... 

ATBN - amine terminated nitrile rubber X - Flory Huggins interaction parameter CPE - carboxylated polyethylene d - width at half height of the copolymer profile given by Kuhn statistical segment length DMAE - dimethyl amino ethanol r - interfacial tension reduction d - particle size reduction DSC - differential scanning calorimetry EMA - ethylene methyl acrylate copolymer ENR - epoxidized natural rubber EOR - ethylene olefin rubber EPDM - ethylene propylene diene monomer EPM - ethylene propylene monomer rubber EPR - ethylene propylene rubber EPR-g-SA - succinic anhydride grafted ethylene propylene rubber... 

Tobolsky, A. V. and DuPre, D. B. Macromolecular Relaxation in the Damped Torsional Oscillator and Statistical Segment Models. Vol. 6, pp. 103 — 127. 

Recendy, Ronova and Pavlova54 suggested a set of relations between the conformational rigidity and some physical properties of the aromatic polymers. The conformational rigidity is correlated to the Kuhn statistical segment A calculated by die Monte Carlo method ... 

Here, b denotes the Kuhn s statistical segment length. The network is represented by a huge chain internally cross-linked at cross-linking points where it touches and at the surfaces of Mf filler particles. The point-like local cross-hnk constraints are easy to handle and can be represented by the term... 

For small deviations from equilibrium, we average r — rm 1 by the statistical segment distribution. For a Gaussian chain which is realized under... 

The longest relaxation time. t,. corresponds to p = 1. The important characteristics of the polymer are its steady-state viscosity > at zero rate of shear, molecular weight A/, and its density p at temperature 7" R is the gas constant, and N is the number of statistical segments in the polymer chain. For vinyl polymers N contains about 10 to 20 monomer units. This equation holds only for the longer relaxation times (i.e., in the terminal zone). In this region the stress-relaxation curve is now given by a sum of exponential terms just as in equation (10), but the number of terms in the sum and the relationship between the T S of each term is specified completely. Thus... 

Here we have chosen the Kuhn statistical segment length (=2q) as the unit for measuring length. The partition function Z of the total chain is given by... 

When all lengths associated with polymers are measured in units of the Kuhn statistical segment length 2q, the thermodynamic functions AF, II, and g, given by Eqs. (19)-(21), contain two molecular parameters N = L/2q and d s d/2q and two state variables c = (2q)3 c and a. Thus, numerical solution to Eqs. (23) and (31) provides ci, cA, and a as functions of N and d. The results for the phase boundary concentrations have been found to be represented to a good approximation by the following empirical expressions ... 

The parameter Cr expresses the effectiveness of the hindrance release by segment fluctuation and varies between 0 and 1. An empirical expression for it as a function of the Kuhn statistical segment number N is given in Sect. 8. Although Cr contributes only to the correction terms in de/Le, fr(de/Le) changes from 1 to 2.56 in the range of allowable values of de/Le. Thus, the factor fr (de/Le) is more important than the factor f (de/Le) in Dx. 

Fig. 3. The dependence of % on the volume fraction of the dry polymer tp2 for i - 0.012 and c = 0. Numbers at curves denote the number of monomers in the statistical segment, s. From Ilavsky [34]...

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