Kuhn statistical segment

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... 

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 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. 

A measure of the stiffness of the amylose molecule in dimethyl sulfoxide can be obtained from the parameters of the various hydrodynamic theories. For example, the length of the Kuhn statistical segment. Am, calculated from Cowie s data is of the order of 95 A., corresponding to 18... 

The increased flexibility of amylose in neutral aqueous solution is further reflected by the low value of the Kuhn statistical segment in this solvent. The value oi Am derived from the viscosity data (21.1 A.) is in fair agreement with that obtained from sedimentation measurements (17.3 A.), and very much less than the figure of 95 A. for amylose in dimethyl sulfoxide. 

Unperturbed Dimenaons.—The most fundamental model of the statistics of a polymer in solution is the linear Gaussian chain, which exhibits the Markovian property that the mean square end-to-end distance o is directly proportional to the number of chain segments i.e. ounperturbed dimensions , and b is the (Kuhn) statistical segment length. 

Fig. 18 Activation energy of p-relaxation in (a) low-molecular weight glasses and (b) linear polymers vs the cohesion energy or cohesion energy of Kuhn statistical segment, respectively [86, 88,103]. (a) (1) Pentanol (2) isopropylbenzene (3) 5-methyl-3-heptanol (4) decalin (5) 1,1-diphenylpropane (6) diethyl phthalate (7) glycerol (8) 6>-terphenyl (9) hexamethyl disolox-ane (10) tetra-a-methylstyrene (11) pentastyrene. (b) (1) Polyethylene (2) polyisoprene (3) poly(dimethylsiloxane) (4) poly(diethylsiloxane) (5) poly(phenylene oxide) (6) poly(ethylene terephthalate) (7) polytetrafluoroethylene (8) polycarbonate (9) polyamide (10) polypropylene (11) polymethacrylate (12) poly(vinyl fluoride) (13) poly(vinyl acetate) (14) poly(vinyl chloride) (15) poly(vinyl alcohol) (16) poly(methyl methacrylate) (17) poly(diphenyl oxypheny-lene) (18) poly(butyl methacrylate) (19) polystyrene (20) polyacrylonitrile (21) poly(a-methylstyrene) (22) poly(cyclohexyl methacrylate) (23) polyimide I (24) polyimide II (25) poly(metaphenylene isophthalamide) (26) polyisobutylene...

In this PU network relatively rigid nanodomains were incorporated, TMP-TDI adducts, as network junctions chemically connected with flexible PPG chains. Each PPG chain (crosslink) consisted on average of about five Kuhn statistical segments. SAXS measurements indicated Bragg s quasi-periodic distribution of rigid junctions with a characteristic size of 6-9 nm in this network. 

The interfacial tension increment. Ay = y yo, was linear with the copolymer volume fraction, calculated for low concentration of the copolymer additive as suggested by theory for concentrations below the CMC. The slope of the fitted line was —37.0, and thus d was estimated to be 38 nm, or 63.5b when the geometric mean of the Kuhn statistical segment lengths of the two segments was used as 0.6 nm. This value of d ( 63.5 monomer units) was about 24% of the contour length of the copolymer chains and, thus, indicated an extended configuration of the copolymer chains. 

Here y N is the degree of incompatibility of the species, k-g, is the Boltzmann constant, T is the absolute temperature, 4> is the average copolymer volume fraction, and b is the Kuhn statistical segment length. Formally, the same expression for yo would be obtained if there were no copolymer chains in the system. 

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