Weight average molecular weight

This quantity is called the weight average molecular weight, reflecting the chemist s customary carelessness about distinguishing between mass and weight, and is given the symbol M. By contrast, the mean, where number fractions are used, is called the number average molecular weight and is given the symbol M .  [c.37]

The weight average molecular weight of a distribution will always be greater than the number average. This is true because the latter merely counts the contribution of molecules in each class, whereas the former weights their contribution in terms of mass. Thus those molecules with higher molecular weights contribute relatively more to the average when mass fraction rather than number fraction is used as the weighting factor. For all polydisperse systems  [c.38]

Next we turn our attention to the distribution of the molecules by weight among the various species. A corollary of this is the determination of the weight average molecular weight and the ratio  [c.295]

The weight average molecular weight of acetal copolymers may be estimated from their melt index (MI, expressed in g/10 min) according to the relation  [c.57]

Polyacrylamides are classified according to weight-average molecular weight (M ) as follows  [c.143]

Typical acryhc polymers have number average molecular weights in the 40,000 to 60,000 range or roughly 1000 repeat units. The weight average molecular weight is typically in the range 90,000 to 140,000, with a polydispersity index between 1.5 and 3.0. The solution properties of the polymer and rheological properties of the dope must be precisely defined for compatibiUty with dope preparation and spinning. The molecular weight of the polymer must be low enough that the polymer is readily soluble in spinning solvents, yet high enough to give a dope of moderately high viscosity.  [c.276]

This polymer can be dissolved in certain high boiling esters at temperatures above 230°C (22), permitting a weight-average molecular weight deterrnination by light scattering. Solution viscosity data suggest that the polymer exists as a slightly expanded coil under similar conditions (23).  [c.366]

Molecular weights of polymers are determined by the weight—average molecular weight, and the number—average molecular weight, M. The  [c.368]

MI is an approximate measure of the weight—average molecular weight logjo (MI) = X logj (M )  [c.368]

Scattering. Use of the classical techniques of small-angle scattering of light and x-rays to study polymer blends has been reviewed (77). Scattering techniques provide a sensitive method for determining whether blends are homogeneous or heterogeneous and to foUow the kinetics of phase-separation processes (78). Small-angle neutron scattering (sans) and reflection have emerged as powerful tools for investigating many aspects of polymer blends (76,79—91). The sans technique can be used to obtain thermodynamic interaction energies for miscible blends however, one of its more unusual aspects is the abiUty to determine conformational information about the components. For example, the radius of gyration of a styrene—acrylonitrile (AN) copolymer containing 19% AN by weight as a function of its weight average molecular weight when blended with a deuterated poly(methyl methacrylate) has been determined (79,83). The chain is slightly more expanded in the blend than the unperturbed chain dissolved in an ideal or 9 solvent, as would be expected for a solvent which is somewhat better than an ideal one. Thus, it is confirmed that the copolymer is moleculady dissolved in PMMA in the same sense as polymers are in low molecular weight solvents this requires mixing at the segmental level for the blend (79,80,83). The sans technique has become an important tool in elucidating the phase behavior and quantifying the interactions in polyolefin blends (88—91). A significant issue in the use of sans for these purposes is that one of the samples generally needs to be deuterated to produce scattering contrast. This can pose some synthesis challenges. Of more serious concern is the fact that deuterated polymers appear to have measurably different interactions with other molecules than their hydrogenous counterparts (86—90).  [c.411]

Polymer solutions are often characterized by their high viscosities compared to solutions of nonpolymeric solutes at similar mass concentrations. This is due to the mechanical entanglements formed between polymer chains. In fact, where entanglements dominate flow, the (zero-shear) viscosity of polymer melts and solutions varies with the 3.4 power of weight-average molecular weight.  [c.435]

Melt and Solution Properties. Melt rheology of PPS is complicated by the high temperatures needed and the requirement that air be excluded to avoid adventitious oxidative curing. One study (44) of the melt rheology of three commercially important classes of PPS, ie, linear and uncured, branched and uncured, and linear and cured, showed the unexpected result that the Newtonian viscosity of linear, uncured PPS increased with the 4.9 power of the weight-average molecular weight, rather than the expected 3.4 power. A homologous series of samples containing increasing amounts of long-chain branching showed increasingly non-Newtonian behavior. This was rationalized on the basis of the branched polymers having higher weight-average molecular weight and broader molecular weight distributions.  [c.446]

Physical. An extensive compilation of physical properties of PS has been given (2,3). In general, a polymer must have a weight-average molecular weight M about 10 times higher than its chain entanglement molecular weight (M to have optimal strength. Below the strength of a polymer changes rapidly with M. However, at about 10 times the strength reaches a plateau region (Fig. 1). For PS, the Af is 18,100 (4). Thus PS having an < 180,000 is generally too britde to be useful. This indicates why no general-purpose mol ding and extmsion grades of PS are sold commercially that have < 190,000.  [c.504]

For some purposes this average may be less useful than the weight average molecular weight defined by which considers the fraction by weight of each molecular size i.e.  [c.41]

One further effect of long chain branches is on flow properties. Unbranched polymers have higher melt viscosities than long-branched polymers of similar weight average molecular weight. This would be expected since the long-branched molecules would be more compact and be expected to entangle less with other molecules.  [c.215]

Typical of thermoplastics (see Chapter 8) the melts are pseudoplastic and also in common with most thermoplastics the zero shear rate apparent viscosity of linear polyethylene is related to the weight average molecular weight by the relationship  [c.222]

M = 45 000-64000, although values may be as low as 40 OTO and as high as 480 000 for the weight average molecular weight. The ratio MJM is usually about 2 for the bulk of commercial material although it may increase with the higher molecular weight grades.  [c.320]

Fig. 31. Evolution of the T-peel strength of roughened styrene-butadiene rubber/polychloro-prene-aromatic hydrocarbon resin blends as a function of the weight average molecular weight of the hydrocarbon resin. Peeling rate = 10 cm/min. Fig. 31. Evolution of the T-peel strength of roughened styrene-butadiene rubber/polychloro-prene-aromatic hydrocarbon resin blends as a function of the weight average molecular weight of the hydrocarbon resin. Peeling rate = 10 cm/min.
LS 5 EV Normalized scattering chromatogram for scattering angle 5° normalization with respect to initial laser intensity and applied sample concentration as a result the area within the selective separation range numerically equals the weight average molecular weight (M ) of the investigated sample  [c.462]

M (true) known weight average molecular weight of broad distributed standard  [c.463]

Weight average molecular weight M =  [c.464]

Narrow distribution polystyrene is the most widely used standard for polymers soluble in organic solvent. Narrow distribution polystyrene standards have been evaluated for the determination of weight average molecular weight of polystyrene by SEC and as long as calibration was constructed by passing through most data points smoothly, no difference in calculated MW among standards from different vendors was noticed (7). Narrow distribution polyethylene oxide (PEO) is one of the most widely used calibration standard for water-soluble polymers and is available in sets of 7 to 10 standards from several vendors. However, the quality of these standards has not been evaluated adequately. NIST has introduced two narrow distribution PEO standards. In this study, the NIST standards are used as a bench mark to evaluate commercial PEO standards.  [c.500]

Figure 7 Influence of the adsorbed dose on the weight-average molecular weight. O = 0.735 = 1.047 = 2.1105 M/L. Figure 7 Influence of the adsorbed dose on the weight-average molecular weight. O = 0.735 = 1.047 = 2.1105 M/L.
The increase in the temperature reduces the viscosity of the polymerization medium which increases the termination reactions. This is attributed to an increase in chain transfer reactions higher than that of propagation reactions [16,51]. Consequently, the weight-average molecular weight of the formed polymer decreases.  [c.127]

Figure 11 shows that the conversion and weight-average molecular weight increases after ceasing irradiation. The copolymer yield seemingly come to an equilibrium within 6 h, the molecular weight continues increasing for nearly 50 h. These may be argued to be structural changes [80], possibly via conformational equilibria [81]. Aggregation [82] and cluster formation [52] may not be neglected. In fact, there is ample evidence on segmental motion of these and related copolymers [83,84].  [c.127]

The efficiency of flocculation of these polyelectrolytes was investigated at different pH and polymer concentrations, valency of cations, and weight-average molecular weight of the polymer. The results are shown in Figs. 12-16,  [c.128]

Figure 16 Influence of polymer concentration and weight-average molecular weight (Mw)j)n the polymer efficiency. = Mw - 5.5 X 10 O = Mw = 3.0 x 10. Figure 16 Influence of polymer concentration and weight-average molecular weight (Mw)j)n the polymer efficiency. = Mw - 5.5 X 10 O = Mw = 3.0 x 10.
Zirconocene (ligand) Activity (kg PP/g catalyst/h) Weight average molecular weight (kg/mol) Melting point (°C)  [c.161]

Weight Average Molecular Weight  [c.319]

The weight average molecular weight (M ) is the sum of the products of the weight of each species present and its molecular weight, divided by the sum of all the species weights  [c.319]

Substituting N,M,- = W, the weight average molecular weight can be defined as  [c.319]

Using this concept, Burdett developed a method in 1955 to obtain the concentrations in mono-, di- and polynuclear aromatics in gas oils from the absorbances measured at 197, 220 and 260 nm, with the condition that sulfur content be less than 1%. Knowledge of the average molecular weight enables the calculation of weight per cent from mole per cent. As with all methods based on statistical sampling from a population, this method is applicable only in the region used in the study extrapolation is not advised and usually leads to erroneous results.  [c.56]

This method follows the ASTM D 1159 and D 2710 procedures and the AFNOR M 07-017 standard. It exploits the capacity of the double olefinic bond to attach two bromine atoms by the addition reaction. Expressed as grams of fixed bromine per hundred grams of sample, the bromine number, BrN, enables the calculation of olefinic hydrocarbons to be made if the average molecular weight of a sufficiently narrow cut is known.  [c.83]

M = average molecular weight of the hydrocarbons in the  [c.161]

Thus the quantitative elemental analysis of the fuel establishes an overall formula, (CH O ) , where the coefficient x, related to the average molecular weight, has no effect on the fuel-air ratio.  [c.179]

Paraffins consist mainly of straight chain alkanes, with a very small proportion of isoalkanes and cycloalkanes. Their freezing point is generally between 30°C and 70°C, the average molecular weight being around 350. When present, aromatics appear only in trace quantities.  [c.285]

Equation (2.39) is the weight average molecular weight as defined in Sec. 1.8. It is important to note that this result. My = M y, applies only in the case of nonentangled chains where 17 is directly proportional to M. A more general definition of My for the case where 17 a is  [c.106]

The limiting low shear or 2ero-shear viscosity T q of the molten polymer can be related to its weight-average molecular weight, by the same  [c.172]

The melt viscosity of a thermoplastic polyurethane (TPU) depends on the weight-average molecular weight and is iafiuenced by chain length and branching. TPUs are viscoelastic materials, which behave like a glassy, brittie soHd, an elastic mbber, or a viscous Hquid, depending on temperature and time scale of measurement. With increasing temperature, the material becomes mbbery because of the onset of molecular motion. At higher temperatures a  [c.343]

Table 6. AWalue Vs Weight-Average Molecular Weight for PVP Table 6. AWalue Vs Weight-Average Molecular Weight for PVP
Glycogen [9005-79-2] the principal carbohydrate food-reserve material in animals, has a stmcture similar to that of amylopectin, ie, it is a branched polymer consisting of linear segments of (1 — 4)-1inked a-D-glucopyranosyl units joined by the (1 — 6) glycosidic linkages that constitute the branch points. All cells of higher animals may contain some glycogen. Because it is in a dynamic state, glycogen is polymolecular with the range of molecular weights depending on the metaboHc state of the tissue. The weight-average molecular weight of rabbit Hver glycogen was reported to be 2.7 x 10 daltons with a range of 6 x 10 to 1.6 x 10 daltons. It contains 0.35% of covalendy-bound protein, a molecule that served as the primer upon which glycogenesis began. The average degree of polymerisation (DP) of the chain segments depends on the source, but the majority of values ate within the range DP 11—14. Glycogen is an amorphous polymer. It is highly soluble and exhibits a fairly ideal hydrodynamic behavior.  [c.477]

The melt index (MI) of polyethylene is also a low shear measurement used in the plastics industry to predict processibiUty and properties. Both MI and Mooney viscosity are related to 2ero shear viscosity and, therefore, the weight average molecular weight (MJ. Mooney viscosity is direcdy proportional to and MI is inversely proportional to M. For this reason, polyethylene MI is usually specified for prediction of the CSM Mooney viscosity. Melt index, however, is not always a good measure of because in most cases it is measured in the non-Newtonian region of the flow curve. The shape and slope in this region are strongly affected by the MWD of the resin. To correct for this, a second MI measurement of polyethylene at a higher shear rate is often measured. The slope of the curve between these points is a function of MWD and may be used, in conjunction with MI, to more accurately predict the CSM viscosity. Increasing the chlorine content of the polymer backbone also increases Mooney viscosity because of increased chain entanglement and intermolecular hydrogen bonding. Generally the Mooney viscosity of the polymer doubles for each 10% chlorine increase at equivalent chain length.  [c.491]

For a specific polymer the melt viscosity is considerably dependent on the (weight average) molecular weight. The higher the molecular weight the greater the entanglements and the greater the melt viscosity. Natural rubber and certain poly(methyl methacrylate) products (e.g. Perspex), which have moleculcO weights of the order of 10 , cannot be melt processed until the chains have been broken down into smaller units by mastication processes. Chain branching also has an effect. In the case of polyethylene and the silicones the greater the branching, at constant weight average molecular weight, the lower the melt viscosity. However, in poly(vinyl acetate) the melt viscosity increases with an increase in branching. It has been suggested that the branch length may be the controlling influence in this. Factors affecting the viscous flow properties of polymers are discussed more fully in Chapter 8.  [c.73]

The influence of polymer concentration on the percent of residual metal concentration [M] was studied at a polymer concentration of 10 mg/1, metal sulphate concentration of 10 gm/1, and pH 6, results are shown in Figs. 12-14. It is clear that [M] decreases with increasing polymer dosage. As the polymer concentration increases, the number of extended segments onto the solution increases. These extended segments, which affect the probability of the segment collision and consequently the probability of forming the floe, increase. This is in agreement with the findings of other investigators [7,10,11,13,17]. The change in the polymer dosage required to bring 0% [M] varies from one type of polymer to another. This is due to the difference in the weight-average molecular weight of the polymer used. Figs. 12-14 show that the polymer concentration for complete precipitation of Mg " is higher than that of Cu. This is due to the difference in the hydration of cations. Increases in the hydration decrease the polymer efficiency. This is in agreement with the findings of Doli-more et al. [14]. They found that the extent of flocculation decreases with increasing thickness of the adsorbed water layer around the cations of the clay particles upon treatment with polymeric flocculants.  [c.130]

See pages that mention the term Weight average molecular weight : [c.38]    [c.437]    [c.490]    [c.130]   
Plastics materials (1999) -- [ c.32 , c.168 , c.216 , c.218 , c.366 ]

Chemistry of Petrochemical Processes (2000) -- [ c.318 ]