Molecular weight distribution theory

Molecular Weight Distribution Theory Blfunctlonal Initiator — In the case of a bifunctional Initiator such as poly(ethylene glycol) tosylate, each initiator end reacts with monomer independently. When the rate of initiation is smaller than the rate of the propagation. Initiation proceeds side by side with propagation. If z monomer units have added to an active end which Initiated at time zero, then ... 

Model Networks. Constmction of model networks allows development of quantitative stmcture property relationships and provide the abiUty to test the accuracy of the theories of mbber elasticity (251—254). By definition, model networks have controlled molecular weight between cross-links, controlled cross-link functionahty, and controlled molecular weight distribution of cross-linked chains. Sihcones cross-linked by either condensation or addition reactions are ideally suited for these studies because all of the above parameters can be controlled. A typical condensation-cure model network consists of an a, CO-polydimethylsiloxanediol, tetraethoxysilane (or alkyltrimethoxysilane), and a tin-cure catalyst (255). A typical addition-cure model is composed of a, ffl-vinylpolydimethylsiloxane, tetrakis(dimethylsiloxy)silane, and a platinum-cure catalyst (256—258). 

Firstly, the classical theories on radical reactivity and polymerization mechanism do not adequately explain the rate and specificity of simple radical reactions. As a consequence, they can not be used to predict the manner in which polymerization rate parameters and details of polymer microstructurc depend on reaction conditions, conversion and molecular weight distribution. 

It is also possible to prepare them from amino acids by the self-condensation reaction (3.12). The PAs (AABB) can be prepared from diamines and diacids by hydrolytic polymerization [see (3.12)]. The polyamides can also be prepared from other starting materials, such as esters, acid chlorides, isocyanates, silylated amines, and nitrils. The reactive acid chlorides are employed in the synthesis of wholly aromatic polyamides, such as poly(p-phenyleneterephthalamide) in (3.4). The molecular weight distribution (Mw/Mn) of these polymers follows the classical theory of molecular weight distribution and is nearly always in the region of 2. In some cases, such as PA-6,6, chain branching can take place and then the Mw/Mn ratio is higher. 

Industrial Engineering Chemistry Research 37, No.7, July 1998, p.2582-91 POLYETHYLENE PYROLYSIS THEORY AND EXPERIMENTS FOR MOLECULAR WEIGHT DISTRIBUTION KINETICS Sezgi N A Cha W S Smith J M McCoy B J California,University... 

Molecular Weight Distributions in Nonlinear Polymers and the Theory of Gelation... 

The critical conditions for the formation of infinite networks will be discussed at the outset of the present chapter. Molecular weight distributions for various nonlinear polymers will then be derived. Experimental data bearing on the validity of the theory will be cited also. 

Molecular weight distribution function for the case where the length of the growth stage is short compared to the residence time in reactor. (Reprinted with permission from Chemical Reactor Theory, by K. G. Denbigh and J. C. R. Turner. Copyright 1971 by Cambridge University Press.)... 

For a theoretical description of crosslinking and network structure, network formation theories can be applied. The results of simulation of the functionality and molecular weight distribution obtained by TBP, or by off-space or in-space simulations are taken as input information. Formulation of the basic pgf characteristic of TBP for crosslinking of a distribution of a hyperbranched polymer is shown as an illustration. The simplest case of a BAf monomer corresponding to equation (4) is considered ... 

Now we compare the above osmotic pressure data with the scaled particle theory. The relevant equation is Eq. (27) for polydisperse polymers. In the isotropic state, it can be shown that Eq. (27) takes the same form as Eq. (20) for the monodisperse system though the parameters (B, C, v, and c ) have to be calculated from the number-average molecular weight M and the total polymer mass concentration c of a polydisperse system pSI in the parameters B and C is unity in the isotropic state. No information is needed for the molecular weight distribution of the sample. On the other hand, in the liquid crystal state2, Eq. (27) does not necessarily take the same form as Eq. (20), because p5I depends on the molecular weight distribution. 

In 1944, Flory (3) noted that the moduli of cross-linked butyl rubbers generally differ somewhat from values calculated from the crosslink density according to the kinetic theory of rubber elasticity. In many cases, the modulus also depends on the primary (uncross-linked) molecular weight distribution of the polymer. He attributed both observations to three kinds of network defects chain ends, loops, and chain entanglements. The latter are latent in the system prior to cross-linking and become permanent features of the network when cross-links are added. 

Theories based on the uniformly effective medium have the practical advantage that they can be extended quite easily to polydisperse systems (227). Viscosity master curves can be predicted from the molecular weight distribution, for example. The only new assumption is that the entanglement time at equilibrium for a chain of molecular weight M in a polydisperse system has the form suggested by the Rouse theory (15) ... 

According to Eq.(8.52), negative values of G at low frequencies occur if Nt becomes proportional to a power of shear rate less than one, a condition which should be attainable at moderate shear rates in concentrated solutions of polymers with narrow molecular weight distribution. Thus, any molecular theory which predicts rj and N1 as functions of shear rate, and which is also consistent with the BKZ and simple fluid theories should automatically yield superimposed moduli which satisfy Eqs.(8.49)-(8.52) without special assumptions about entanglement mechanisms. 

Manfee, E., and W. L. Peticolas Polymers and the theory of numbers Molecular weight distribution from rheological measurements. Nature 189, 745 (1961). 

Since the dilute solution theory is considered as the basis for the indicated treatment, it will receive considerable attention. Influences of several parameters as molecular weight, molecular weight distribution, thermodynamic and kinetic chain stiffness, intramolecular hydrodynamic inter-action, optical properties of the chain and solvent power will be considered. 

It is observed that Bueche s equation in combination with the g1/2 rule explains the results of this work whereas in combination with g3/2 it does not. The correction to g for polydispersity brings closer the agreement between the data and the seventh power relation. The difference of a few percent between the expected and observed slopes of 7 and 6.4 may be attributed to an undercorrection for polydispersity in this regard according to Graessley s findings current theories do not sufficiently account for the reduction in viscosity with polydispersity, whether the Beasley or the Stockmayer molecular weight distribution is employed (29). 

F 4. — Molecular weight distributions in nonlinear polymers and the theory of gelation. Principles of Polymer Chemistry, 347 ff. New York Cornell University Press 1953. 

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