10_Polymer_Physics_02 - 1.3 Molecular sizes and shapes and...

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1.3.2 Molecular Weight * Typical synthetic polymer ~ wide distribution of chain length Depending on the synthesis conditions, the distributions are varied. • Mixture of chains of different lengths • Concept of average is employed to describe the molecular weights How to define average? 1.3 Molecular sizes and shapes and ordered structures
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For a discrete distribution of molecular weights, 1. Average molecular weight, can be defined in various ways, when weight is given by, M = = = = = = N i i i N i i N i i N i i i n M W W N M N M 1 1 1 1 ) / ( = = = = = = N i i N i i i N i i i N i i i w W M W M N M N M 1 1 1 1 2 = = = = = = N i i i N i i i N i i i N i i i z M W M W M N M N M 1 1 2 1 2 1 3 Number average mol. Wt. Weight average mol. Wt. Z- average mol. Wt. i i i M N W =
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– Number Average Molecular Weight gives the same weight to all polymer lengths, long and short. – Measured by Osmometry, end-group titration, colligative properties. ... ... 3 2 1 3 3 2 2 1 1 + + + + + + = = N N N M N M N M N N M N M i i i n 000 , 260 ) 1 3 5 4 1 ( ) 700 ( 1 ) 500 ( 3 ) 200 ( 5 ) 100 ( 4 ) 50 ( 1 ... ... 3 2 1 3 3 2 2 1 1 = + + + + + + + + = + + + + + + = = n n i i i n M K K K K K M N N N M N M N M N N M N M Example, What is the molecular weight of a polymer sample in which the polymers molecules are divided into 5 categories. Group Frequency 50,000 1 100,000 4 200,000 5 500,000 3 700,000 1 Number average mol. wt. excerpted from Pro. Joseph Greene of CHICO
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– The data yields a nonsymmetrical curve (common) – The curve is skewed with a tail towards the high MW –T h e M n is determined experimentally by analyzing the number of end groups (which permit the determination of the number of chains) – The number of repeating units, N, can be found by the ratio of the M n and the molecular weight of the repeating unit, M 0 , for example for polyethylene, M 0 = 28 g/mole – The number of repeating units, N, is often called the degree of polymerization, DP. – DP relates the amount of monomer that has been converted to polymer. 0 M M N n = excerpted from Pro. Joseph Greene of CHICO
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Weight average mol. wt. ... ... 3 3 2 2 1 1 2 3 3 2 2 2 2 1 1 2 + + + + + + = = M N M N M N M N M N M N M N M N M i i i i w Weight Average Molecular Weight, M w – Favors large molecules versus small ones – Useful for understanding polymer properties that relate to the weight of the polymer, e.g., penetration through a membrane or light scattering, sedimentaion velocity and small angle neutron scattering. excerpted from Pro. Joseph Greene of CHICO
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Z- average mol. wt. ... ... 2 3 3 2 2 2 2 1 1 3 3 3 3 2 2 3 1 1 2 3 + + + + + + = = M N M N M N M N M N M N M N M N M i i i i z - Emphasizes large molecules even more than Mw - Useful for some calculations involving mechanical properties. - Method uses a centrifuge to separate the polymer (sedimentation equilibrium) Homework: submit it within two weeks Calculate the number-average, weight average, z- average, and plot frequency vs. molecular weight curve, polydispersity and mark the averages on the plot) Group Frequency 20,000 1 50,000 3 100,000 5 200,000 7 500,000 13 700,000 8 900,000 6 1,000,000 2 excerpted from Pro. Joseph Greene of CHICO
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Molecular Weight Distribution represents the
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10_Polymer_Physics_02 - 1.3 Molecular sizes and shapes and...

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