Theoretical observations on spinodal decomposition of polymer solutions
Abstract
In systems showing spinodal decomposition, it is to be expected that a certain dimension Dm will be realized most frequently. Although most concentration fluctuations present increase in amplitude with time, the rate of increase depends upon the wavelength of the fluctuation, so that some fluctuations will grow much more rapidly than others; as a result, there will be a fairly uniform dimension throughout the system. In order to obtain an estimate of the dimensions to be expected in the system PPO®-caprolactam, some theoretical observations have been combined to yield Dm values of the order of 1 μ, depending upon the temperature below the spinodal where the decomposition sets in.
Résumé
Dans le cas des systèmes qui présentent une décomposition spinodale, on doit s'attendre à ce qu'une certaine dimension Dm soit la plus fréquemment réalisée. Bien que la plupart des fluctuations de concentration ont une amplitude qui s'accroît avec le temps, la vitesse d'accroisement dépend de la longueur d'onde de la fluctuation, de telle sorte que certaines fluctuations s'accroissent beaucoup plus rapidement que d'autres; il en résulte l'existence d'une dimension pratiquement uniforme au sein du système. Dans le but de pouvoir estimer les dimensions auxquelles on doit s'attendre pour le système PPO®-caprolactame, on a réussi quelques observations théoriques pour obtenir des valeurs de Dm de l'ordre du micron, en tenant compte de la température inférieure à la température spinodale à laquelle la décomposition a lieu.
Resumen
Nei sistemi che presentano decomposizione spinodale, ci si dovrebbe aspettare che una certa dimensione Dm si realizzi più di frequente. Sebbene molte fluttuazioni di concentrazione aumentino in ampiezza con il tempo, la velocità dell'aumento dipende dalla lunghezza d'onda della fluttuazione, così che alcune fluttuazioni aumentano più rapidamente di altre; come risultato ci dovrebbe essere una dimensione quasi uniforme attraverso il sistema. Per ottenere un'idea delle dimensioni da aspettarsi nel sistema PPO®-caprolattame, sono state combinate alcune osservazioni teoriche per ottenere valori Dm dell'ordine di un micron, dipendenti dalla temperatura al di sotto della quale ha luogo la decomposizione spinodale.
Zusammenfassung
In Systemen, die spinodale Zersetzung zeigen, ist zu erwarten, daβ eine bestimmte Dimension Dm besonders häufig auftritt. Obwohl die meisten vorliegenden Konzentrationsschwankungen in ihrer Amplitude mit der Zeit zunehmen, hängt die Geschwindigkeit der Zunahme von der Wellenlänge der Schwankung ab, sodaβ einige Schwankungen sehr viel rascher zunehmen als andere. Daraus ergibt sich eine ziemlich gleichmäβige Dimension im ganzen System. Um eine Abschätzung der zu erwartenden Dimensionen im System PPO®-Caprolactam zu erhalten, wurden einige theoretische Beobachtungen Kombiniert und ergaben Dm Werte in der Gröβenordnung von 1 μ, in Abhängigkeit von der Temperatur unterhalb der Spinodalen bei der die Zersetzung beginnt.
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