Indice di polidispersione

L'indice di polidispersione è una misura dell'uniformità di distribuzione dei pesi molecolari in un determinato polimero. La polidispersità viene espressa tramite un indice calcolato dal rapporto tra la massa molare media ponderale e la massa molare media numerica del polimero, essendo:

massa molare media numerica: $M_{n}=\sum n_{i}M_{i}/\sum n_{i}$
massa molare media ponderale: $M_{w}=\sum w_{i}M_{i}/\sum w_{i}=\sum n_{i}M_{i}^{2}/\sum n_{i}M_{i}$

in cui:

$M_{i}\!\$ = massa molecolare dell'i-esima molecola;
$n_{i}\!\$ = numero di moli delle molecole aventi massa molecolare pari a $M_{i}\!\$ ;
$w_{i}\!\$ = massa delle molecole con massa molecolare pari a i.

Siccome la massa molare media ponderale è sempre maggiore della massa molare media numerica, l'indice di polidispersività (essendo pari al rapporto M_w/M_n) assume sempre valori maggiori di 1.

Il termine "monodisperso" viene per convenzione utilizzato fino a valori di indice di polidispersività minore a 1,1.^[1] In caso contrario il polimero è detto "polidisperso".

Nel caso di polimeri ottenuti tramite polimerizzazione a stadi si hanno valori dell'indice di polidispersione più bassi (intorno a 2), mentre nel caso di polimeri ottenuti tramite polimerizzazione a catena si hanno valori di polidispersione più elevati.

Esempio di calcolo

Si considerino 300 kg di materiale polimerico formato da:

100 kg aventi massa molare media di 30000 g/mol (numero moli = 100000 g / 30000 g/mol ≈ 3,33 moli)
100 kg aventi massa molare media di 60000 g/mol (numero moli = 100000 g / 60000 g/mol ≈ 1,67 moli)
100 kg aventi massa molare media di 90000 g/mol (numero moli = 100000 g / 90000 g/mol ≈ 1,11 moli).

Si ha:

M_n = (3,33×30000 + 1,67×60000 + 1,11×90000) / (3,33 + 1,67 + 1,11) ≈ 49099 g/mol
M_w = (100000×30000 + 100000×60000 + 100000×90000) / (100000 + 100000 + 100000) ≈ 60000 g/mol

da cui:

polidispersività = M_w / M_n = 60000 / 49099 = 1,22

Note

^ P. Atkins, J. De Paula, "Physical Chemistry", Oxford University Press, 2006 (ottava ed.), pp. 655 ISBN 978-0-19-870072-2

Bibliografia

H. Allcock, F. Lampe, J. Mark, "Contemporary Polymer Chemistry - 3rd Edition", Prentice Hall, 2003, ISBN 978-0-13-065056-6.

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Portale Chimica

Portale Metrologia

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