Molecular weight , average molar mass

Figure 6.10 Effect of CITREM on the molecular and thermodynamic parameters of maltodextrin SA-2 (DE = 2) in aqueous medium (phosphate buffer, pH = 7.2, ionic strength = 0.05 M 20 °C) (a) weight average molar mass, Mw (b) radius of gyration, Ra (c) structure sensitive parameter, p, characterizing die architecture of maltodextrin associates (d) second virial coefficient, A2 or A2, on the basis of the weight ( ) and molal (A) scales, respectively. The parameter R is defined as the molar ratio of surfactant to glucose monomer units in the polysaccharide. The indicated cmc value refers to the cmc of the pure CITREM solution. Reproduced from Anokhina et al. (2007) with permission.

To demonstrate it, we purposely chose two hyperbranched samples and their molecular parameters [the weight-average molar mass (Mw), polydisper-sity index (M /Mn), and average hydrodynamic radius ((f h))l, are summarized in Table 5.1, where a linear polystyrene sample was used as an internal reference to calibrate the concentrations of hyperbranched chains before and after the ultrafiltration. 

Number-average molar masses were determined using a vapor pressure osmometer (VPO) (Hitachi 117 Molecular Weight Apparatus) at 54.8 0.1°C in toluene (Fisher Scientific, certified A.C.S.) which was distilled from freshly crushed CaH2. The VPO apparatus was calibrated with pentaerythritol tetrastearate (Pressure Chemical). Gel permeation chromatographic (GPC) analyses were performed in tetrahydrofuran by HPLC (Perkin-Elmer 601 HPLC) using six y-Styragel columns (106, 105, 10l, 103, 500, and 100 A) after calibration with standard polystyrene samples. 

Typical mechanical properties, such as tensile strength, vary significantly with molecular weight within the range of the real macromolecules. As Eq. (2.2) applies to these properties (number-average molar mass being important), it indicates that the number of chain ends is a preponderant factor. 

This is the Mark-Houwink equation, where the formal dimension of K is equal to cm3/g x (g/mol)a. In general, however, K is tacitly expressed and tabulated in the same dimension as [r ] and the resulting polymer molecular weight M is then expressed in g/mol. For polydis-perse polymers, M is replaced by Mv the so-called viscosity-average molar mass, so that... 

The experimental dependence M = /(V), i.e. the classical SEC calibration curve usually obtained by using narrow standards, in such a case can be obtained directly without calibration from the on-line LS detector. By combining the experimental function M = /(V) and the concentration profile (from DRI), one can construct the complete MMD of the HA sample. The differential and cumulative MMD of a high molar mass HA sample (Mw = 652 kDa, D = 2.1) are shown in Fig. (10). Starting from the initial MMD, the molecular weight averages and dispersity index (Mn, Mw, Mz, and D) could be easily calculated using the appropriate definitions. 

Weight average molecular weight may be experimentally determined by any method in which molecular size or molar mass is the parameter being measured (e.g., light scattering or ultracentrifugation). 

The mass of the linear polymer chain is thus related directly to the number of monomer units incorporated into the chain (DP) and will be Mq x DP, where Mq (g/mol) is the molar mass of the monomeric repeat unit. Thus, if all chains grew to exactly the same DP, then Mq X DP, would be the molar mass of the polymer. If the end groups on the chain can be readily and uniquely analysed, then an average molar mass, M , or number-average molecular weight (as discussed in the next section) can be immediately determined since, if there are amol/g of end group A and hmol/g of end group B then... 

Linear polymers are usually characterized in solution. However, if enough crosslinking has occurred, such as in the vulcanization of elastomers, the polymer will swell but cannot dissolve in typical solvents. Then, it is impossible to derive molar mass (molecular weight) information from solution behavior. However, the average molar mass of the chains in the polymer network can be determined from swelling (1,2). 

Banthia et al. [44] first performed the polymerization of ethyl hexyl acrylate in DEP conditions (Table 6) but without using any solvent. The calculated carboxy functionalities were around 2 and the molecular weights were about 104. The number-average molar masses (Mn) were unexpectedly high for DEP conditions and were probably due to the bulk conditions. 

When a vapor is absorbed in a solvent of high molecular weight, the molar flow rate of liquid wiO be much less than if water were used at the same mass velocity. However, the coefficient kji, which is based on a mole-fraction driving force, also varies inversely with the average molecular weight of the liquid. 

In order to quantify the chain length, the molar mass (or molecular weight) must be defined statistically. The number average molar mass, M, is given by ... 

For the polyesterification reaction between diethylene glycol and adipic acid, calculate the number-average molecular weight of the polyester that is formed when the extent of reaction p is equal to 0.90. Note that, for condensation polymers that are synthesized from two reactants, half the average-molar-mass of the repeat unit is used to calculate the degree of polymerization. 

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