Thermokinetics of formation of ordered structures in polymer solutions and gel

A general approach is proposed a11owing the reduction to a 'common dcnominator' of different forms of formation of ordered structurcs in polymer-solvent systems. This 'common denominator' results from thc combination of the equivalence principle of thcrmokinctics and the concept of diphility of macromolecules. In the first sections the discussion dcals with a precise definition of order and with the foundation ofthe equivalence principle and related physical formalisms. It is shown that the consideration of any mode of structure formation can be reduced to the analysis of phase diagrams and free energy-temperature diagrams, the possibility of such reductions being connccted with two main assumptions (supported by all known experimental data): (i) Due to inherent diphility the Flory-Huggins parameter x 1 can change continuously or discontinuously with the concentration of components leading to the occurrence of preferential chain conformations or abrupt intramolecular conformational transitions. In cases of pronounced explicit diphility (in random or block copolymers) the preference of interactions also Ieads to intramolccular segregation which on increasing polymer concentration develops as a superrnolccular ordcr (il) One can connect these conformational transformations with the dependence of Flory's flexibility parameter f on x1• Taking into account this dependence makes it possible to interpret identically 'antiplastification' phcnomena, the formation of liquid crystalline mesophases with different morphologies and the formation of binary crystals. Hence, various manifestations of molccular and supermolecular forms of ordering in solutions and gels can be treated by analogy with the usual polymorphism in polymers, in the same way as in the Flory-Mandelkcrn crystallization theory. The equivalence principle allows us to consider from quite similar positions the nucleation and growth of crystals or liquid crystals in the presence of external fields. In these cases the flexibility parameter f turns out tobe dependent on the extcrnal ficld and all further considerations can be reduced to the already analysed situation with variable and interdependent x1 and .f parameters. A more profound analysis shows that this equivalence is not formal but reflects the real state of events. The uncoiling of macromolecules in a shear or longitudinal field and thc increase of their interactions means in reality the increase of the interaction parametcr z1 and ultimately thc loss of solubility, or desolvation. The analysis from those positions of a large amount of experimental data shows that in some cases organized structures may exist only in the presence ofa 117 S. FRENKEL solvent which stabilizes them thermodynamically rather than only stimulates kinetically their formation. When organized structures are formed due to external fields they can persist on the elimination of the field andremoval of the solvent, on condition that the energy 'pumpcd over' in the system from the cxternal field is compensated for as the latent crystallization heat (i.e. is simply used for crystallization in the strict sense ofthc word).ln the opposite case (in an atactic polymer) the oriented state is unstable due to developing internal stresses.ln special cases thesc stresses Iead to an 'orientat.ional catastrophe' -the sclf-annihilation of the sample. I NTRODUCTORY NOTES 1.1 On the concept of order in polymers Before summarizing the different data presented at this Symposium one must try to make some general statements about what we understand as "order' in polymer-solvent systems. This is necessary not only to avoid possible confusion and misunderstanding but also to Iimit oneself to the discussion of the most realistic and important (or, maybe, typical) cases of ordered structures formation. Probably the first Iimitation must be connected with the range of order. Although in discussing molecular and supermolecular order in polymers many authors include in the definition of order short range ordcr, for instance in amorphous polymers, this does not seem to be correct or in accord with the generat principles of molecular physics. Of course the appearance of short range order in the liquid state is a necessary step in the transition from the total disorder presented by the gaseous state to a total order which is attainable only in cases of covalent crystals ofthe diamondtype (which immediately returns us to polymers, the non-covalent simple molecular crystals heing always imperfcct !). On the other band, one still makes a distinction between ordered and unordered simple liquids,for instance liquid crystals and isotropic liquids, some anisotropic liquids being intermediates within the liquid state. which is an intermediate state itself. Thus both everyday logic and a need for correct formulations Iead us to the long range order as a 'representative of Order' in polymer-solvent systems These didactic problems that I have mentioned very superficially are of the samekindas the problern of comparison ofliquids with gases and/or solids 1 . In the case of polymers an additional peculiarity, both physical and didactic. immediately arises, the polymer chains per se (even atactic) presenting a sort of unidimensional order the range of which is determined by the degree of polymerization. However, if we adopt Huggins's struction concept 2 to dcscribe not only the molecular but also the supermolecular mode of distribution of chain units in space, then most difficulties can be avoided, and we come back to the definition of order as some kind of long range packing, the structons being formed by repeating units, chain scgments or, in some cases. by the whole macromolecules. Here, by 'packing' we denote only the type of spatial distribution of characteristic units. without further Iimitations concerning immobilization, or mode ofthermal motion, or closeness (ofpacking) etc. The given definition of order includes three-dimensional crystalline lattices 118 THERMOKINETICS OF FORMATION OF ORDERED STRUCTURES as weil as systems with only lateral or only longitudinal (or both) long range order. Thus, it includes automatically every kind of liquid crystalline mesophase. In addition- and this is important-one can take into account different Ievels of order, the role of 'elementary units' being played in those cases by crystallites, fibrils or other morphoses having a sufficient amount of internal long range order. Such an approach will Iead us to the concept of structons of 'higher ranges' which coincides in sense with Hosemann's paracrystalline concept of matter 3 . Two more words should be written about the magnitude of structural units that we still are allowed to call ordercd. Just as in the case of heterophase fluctuations 1 existing in equilibrium with the main phase, one should start with stablc crystallization nuclei which for some reason or other cannot grow. polyvinyl alcohol in water giving a most striking example of such behaviour. One can treat these nuclei a~ 'frozen' heterophase fluctuations, and later we shall discuss their nature in some detail. As to the linear dimensions of theseminimal ordered units, the criterion of order will be connected only with the possibility or impossibility of checking the presence of order by means of x-ray or electron diffraction. 1.2 The thermokinetic approach By thermokinetics I mcan the physical kinctics of phase transitions and changes in order of polymer systems. However, the term by itselfhints at some kind ofhybridization ofthermodynamics and physical (andin some cases also chemical) kinetics. One can alternatively define thermokinetics as a form of statistical mcchanics where the partition function and a11 the relatcd values are treated from the structural point of view. Correspondingly, one must consider the time derivatives ofthe partition function or other time-dependent external or internal parameters, forin reality there exist no physical structures that can change instantaneously. Thus the mentioned time derivatives of the partition function (and consequently of free energy, entropy, etc.) and other time dependent factors must figure explicitly in the equations describing phase transitions, changes in phase equilibria andin general any changes in any systems under the influence of any kind of extemal fields. In this sense thermokinetics is not 'tied' specially to polymer systems. However, if for ordinary systems (as for instance in the kinetic theory of gases) these time-dependent factors play a part of only small corrections that can be usually neglected, in polymer systems these 'corrections' may turn outtobe the dominating factors defining both the character ofthe transition and the morphology (and related properties) ofthe resulting state. Th us, I try to advance a concept rather than a new term. The source of this concept can be found in the K inelic theory of liquids 1 , the kinetic theory of phase transitions being a specific part of the generat theory. The thermokinetic approach to polymer systems as an extension of the above mentioned theory to any kind of structural changes was first proved by the author and G. K. Elyashevich in two papers4 · 5 where the necessary details can be found. In what follows the sameapproachwill be used to discuss some typical cases of formation of order in polymer solutions and gels. It should be added that some of the confusion concerning the phase 119 S. FRENKEL transitions in polymers is largely due to the fact, usually neglected, that polymerization itself is a very specific and fundamental phase transition involving at least three groups of sy