Folded chain crystals as micro-phases

Summary A thermodynamic treatment of homo-polymer systems out of linear chains with folded chain crystals is developed outgoing from appropriate models for single component systems. An expansion of thermodynamics to multi-micro-phase systems the structure of which is partially or totaly frozen is indispensable. General properties of melt crystallized homopolymers with folded chain crystals can be recognized indeed when the thermodynamic formalisms developed are applied.

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Zusammenfassung Das Schmelzen in polymeren Einteilchensystemen mit Faltungskristallen einheitlicher Dicke kann thermodynamisch als Umwandlung 1. Ordnung in einer Richtung behandelt werden, wenn die Faltungslänge bis zur Umwandlungstemperatur konstant bleibt (Faltungslänge als innerer Zusatzparameter). Eine wesentliche begriffliche Erweiterung ist für eine phänomenologische Beschreibung mit den Mitteln der Thermodynamik unumgänglich, wenn eine Faltungskristallit-Dickenverteilung existiert, weil dann prinzipiell nur noch partielle Koexistenz bestimmter Fraktionen metastabiler autonomer Mikrophasen mit der Schmelze möglich ist. Partielles Aufschmelzen und Rektistallisation können so dann auch in Betracht genommen werden. Die entwickelten Konzeptionen bewähren sich in der Anwendung auf bekannte Experimente.

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Notation g^c(y);g^m(Y) molar Gibbs-free energy of a chain of a lengthy within an extended chain crystal and the melt rsp - g_o^c;g_o^m molar free enthalpy of the unit in the crystal lattice and the melt rsp - g(y,y, f) molar Gibbs-function of an ideally folded chain crystal with the fold heighty_f - gco(y, y_ef,y_f) molar free enthalpy of the crystal corey_co - g₀^ex((y_ef) excess free enthalpy of the longitudinal layers of folded chain crystals - g^f(y_ef,g_o^ex) molar free enthalpy of the longitudinal layers of the folded chain crystals - g^tot molar free enthalpy of a chain of the lengthy within a folded chain crystal with longitudinal layers - h_o^1c,h_o^m molar enthalpy of the chain unit within the crystal lattice and the melt rsp - h =h_o^m -h_o^c molar heat of fusion of the unit - C_p=C_p^m -C_p^c difference of the molar specific heat of a unit within the melt and within the chain crystal - h^D molar defect enthalpy of local defects within the crystal lattice - h^D molar defect enthalpy of the unit - s_o^c,s_o^m molar entropy of the chain unit within the crystal lattice and the melt rsp - s_c^m conformational entropy of a chain in the melt - s_gk conformational entropy of a chain of lengthy within a super-lattice as indicated in figure 5, - s molar entropy of fusion of the melt - s_n^c nematic configurational entropy - T absolute temperature - T_M melting temperature of extended chain crystals of infinite size - T_M(y) melting temperature of extended chain crystals containing only chains of the lengthy - T_M (y, y_f) melting temperatureof folded chain crystals of the thicknessy_f composed of chains of the lengthy - T_M(y_f) melting temperature of folded chain crystals of the thicknessy_fy - _eh excess free enthalpy of the chain ends occupying crystallographic places - _ef excess free enthalpy of a single fold loop - z coordination number of the lattice - 7 Euler's constant - R Boltzmann's constant - y number of chain units - y_f height of lamelliform folded chain crystals - f=(y/y_f - 1) number of fold loops of a chain of a lengthy when being built into a folded chain crystal of the thicknessy_f - y_co thickness of the crystal core of the simplified twophase model - y_et average thickness of the surface layers of folded chain crystals - N_c number of crystallized units of a chain of the lengthy - x_c molar number of crystallized units of a chain of the lengthy - x_nc molar number of noncrystallized units - excess free enthalpy parameter - (y_f) thickness distribution of the fold heightsy_fWith 15 figures and 2 tables