Molecular weight infinite

In some cases of multifunctional monomers the possibility exists for branches on branches, which ultimately result in cross-linked products and effectively infinite molecular weights well before p reaches unity. 

The value of a to be used in these expressions is given by Eq. (5.45) for the specific mixture under consideration. At the point of gelation - l/(f- 1) according to Eq. (5.46). Equation (5.55) shows that n becomes infinite at this point while n remains finite. This merely means that there are still many molecules present at the gel point in addition to the network molecule of essentially infinite molecular weight. The ratio h /n indicates an immense expansion of the degree of heterogeneity as a ->. Expressions are also avail-... 

B = 0 when x = 1/2, a condition we have already seen [Eq. (8.60)], corresponds to a critical value of x for a copolymer of infinite molecular weight. For finite molecular weights this condition is not quite a threshold for precipitation, but is close to it. Polymer-polymer contacts are sufficiently favored over polymer-solvent contacts that a chain of infinite length would undergo phase separation. 

T is the glass-transition temperature at infinite molecular weight and is the number average molecular weight. The value of k for poly(methyl methacrylate) is about 2 x 10 the value for acrylate polymers is approximately the same (9). A detailed discussion on the effect of molecular weight on the properties of a polymer may be found in Reference 17. 

The value for the heat of fusion of PPS, extrapolated to a hypothetical 100% crystalline state, is not agreed upon in the literature. Reported values range from approximately 80 J/g (19 cal/g) (36,96,101) to 146 J/g (35 cal/g) (102), with one intermediate value of 105 J/g (25 cal/g) (20). The lower value, 80 J/g, was originally measured by thermal analysis and then correlated with a measure of crystallinity deterrnined by x-ray diffraction (36). The value of 146 J/g was deterrnined independendy on uniaxiaHy oriented PPS film samples by thermal analysis, density measurement via density-gradient column, and the use of a calculated density for 100% crystalline PPS to arrive at a heat of fusion for 100% crystalline PPS (102). The value of 105 J/g was obtained by measuring the heats of fusion of weU-characterized linear oligomers of PPS and extrapolation to infinite molecular weight. 

Advanced Thermoplastics Materials. Thermoplastics and linear plastics of finite molecular weight that can be fabricated into very complex stmctures by hot melt or injection mol ding are different from the thermoset materials that require cross-linking to build up infinite molecular weight to form network (cross-link) stmctures. Advances in thermoplastic engineering materials include amorphous thermoplastics, crystalline thermoplastics, Hquid crystal thermoplastics, and fluorinated thermoplastics (see Engineering plastics). 

It should be noted that polystyrene with a number average molecular weight of 50000 has a Tg only about 2°C less than would be expected of a polystyrene of infinitely high molecular weight. Hence increasing the molecular weight beyond this point in order to raise the Tg would not be very effective and at the same time it would lead to large increases in melt viscosity. 

UK. = Light key component in volatile mixture L/V = Internal reflux ratio L/D = Actual external reflux ratio (L/D) ,in = Minimum external reflux ratio M = Molecular weight of compound Mg = Total mols steam required m = Number of sidestreams above feed, n N = Number of theoretical trays in distillation tower (not including reboiler) at operating finite reflux. For partial condenser system N includes condenser or number theoretical trays or transfer units for a packed tower (VOC calculations) Nb = Number of trays from tray, m, to bottom tray, but not including still or reboiler Nrain = Minimum number of theoretical trays in distillation tower (not including reboiler) at total or infinite reflux. For partial condenser system,... 

The subscripts 1,2,3 refer to the main solvent, the polymer, and the solvent added, respectively. The meanings of the other symbols are n refractive index m molarity of respective component in solvent 1 C the concentration in g cm"3 of the solution V the partial specific volume p the chemical potential M molecular weight (for the polymer per residue). The surscript ° indicates infinite dilution of the polymer. 

A wide range of polyacrylic acids (PAAs), polymethacrylic acids (PMAAs), polyacrylamides (PAMs), their salts and homo-, co-, and terpolymer derivatives are available from a great many manufacturers around the world today. Polyacrylates especially are a backbone of BW chemical formulations and are manufactured with an almost infinite variety of average molecular weights (MWs), MW distributions, activity strengths, and other characteristics. 

Extrapolate the data to infinite dilution to obtain a value for the molecular weight of the polymer. (Note that an average molecular weight is obtained since the polymer consists of a mixture of molecules of different chain lengths.)... 

Finally we would like to draw attention to low molecular weight results and their analysis on the basis of surface nucleation theory. The theory was originally developed for infinitely long chains and cannot easily be applied to extended or once-folded chain crystallization. Therefore any discrepancies in this area would not be surprising and would not discredit the theory at higher molecular weights. 

An infinite set of moments is theoretically necessary to describe a molecular weight distribution but as a practical matter, knowing moments 0, 1, and 2 is usually adequate. The initial condition for all the moments is ii = 7o at T = 0. Solution gives... 

If the denominator in equation 12 is less than or equal to zero, the mixture has gelled. In this case, the weight average molecular weight is infinite. In the absence of the self-condensation reaction - 0), the gel point is given by ... 

Rg,6 is the radius of giration in the 6-state assumed to correspond in polyelectrolyte systems to the value extrapolated to infinite salt concentration. The relation of Benoit-Doty for high molecular weights gives ... 

---