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Chapter 8. Measurement of molecular weight and size 8.1. End-group analysis 8.2. Colligative property measurement 8.3. Osmometry 8.4. Gel-permeation chromatography 8.5. Ultracentrifugation 8.6. Light-scattering methods 8.7. Solution viscosity and molecular size Molecular weights of polymers can be determined by chemical or physical methods of functional-group analysis. They are measurement of the colligative properties, light scattering, or ultracentrifugation; or by measurement of dilute-solution viscosity. Molecular weights can be calculated without reference to callibration by another method. Dilute-solution viscosity is not a direct measure of molecular weight and empirically related to molecular weight for many systems. All methods require the solubility of polymer, involve extrapolation to infinite dilution, and operate in a Θ solvent in which have ideal-solution behaviour. Typical polymers consist of mixtures of many molecular species and molecular weight methods always provide average values. The sum of all molecular species of the number of moles Ni of each species: ∞ ∑Ni i=1 The total weight of the sample, w, = the sum of the weights of each molecular species ∞ ∞ w=∑wi=∑NiMi i=1 i=1 The number-average molecular weight, M molecular weight as n weight of sample per mole ∞ ∑NiMi M = w = i=1 n ∞ ∞ ∑Ni ∑Ni i=1 i=1 8.1. End-group analysis The end-group analysis needs the information about the number of determinable groups per molecule. This method is not suitable for high molecular weight because the fraction of end groups becomes too small to measured with precision (>25,000). Condensation polymers End-group analysis in condensation polymers usually involves chemical methods of analysis for functional groups. Examples: Carboxyl groups in PE and in polyamides are titrated with base in an alcoholic or phenolic solvent. Amino groups in PA are titrated with acid Hydroxyl groups is reacted with a titratable reagent
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