Polymer crystallization thermal fluctuations

Crystallization of polymers is an activated process that may be influenced by the presence of mechanical stresses and external gradients. Clusters are formed at the expense of the metastable phase due to the presence of thermal fluctuations. The process can be modeled by a particle crossing a free energy barrier, whose height depends on the interactions and the external drivings, upon the intervention of... 

The unordered (amorphous) state of aggregation in which the polymer chains also assume random conformations represents one extreme in the physical state of the polymer. This is the state that exists in such amorphous states as solution, melts, or some solids, the randomness being induced by thermal fluctuations. The other extreme is the case where the molecules are able to pack closely in perfect parallel alignment as is found in those polymers that exhibit fibrous behavior— that is, in those possessing a high degree of crystallinity and crystal orientation. In between these two extremes of amorphous and crystalline polymers there is a wide spectrum of polymeric materials with different degrees of crystallinity and amorphous character. These are called semicrystalline. 

A procedure is described that can measure optical phase retardations of birefrigent materials with a resolution 2x10-4 radians. The method relies on phase modulation with alternate right and left handed circularly polarized light. Phase sensitive detection is employed to reduce noise and thermal fluctuations in the optics and light source. The method is useful in Frederik s transition measurements to determine the elastic constants of weakly birefringent polymer liquid crystals with long equilibration times. 

When LCEs are synthesized in the absence of external fields, so-called polydomain LC elastomers are obtained, which show macroscopically isotropic properties similar to polycrystalline materials. This resembles, e.g., bulk material of a low molar mass liquid crystal, where thermal fluctuations prevent a uniform director orientation over the whole sample. For nematic elastomers the overall isotropic behavior also indicates an overall isotropic conformation of the polymer chains, which is the consequence of the maximization of the chain entropy. 

Polymer crystallization can be roughly divided into two sequential processes crystal nucleation and crystal growth. When the sizes of ordered domains generated by thermal fluctuations become so large that the trend to increase the surface free... 

Lekkerkerker H, Vroege G (1993) Lyotropic colloidal and inacroinolecular liquid crystals. Philos Trans R Soc Lond Ser A Phys Eng Sci 344(1672) 419-440 Ma Y, Hu W, Wang H (2007) Polymer immiscibility enhanced by thermal fluctuations toward crystalline order. Phys Rev E 76(3) 031801... 

A final consideration is that the Argon theory essentially regards yield as nucleation controlled, analogous to the stress-activated movement of dislocations in a crystal produced by the applied stress, aided by thermal fluctuations. The application of the Eyring theory, on the other hand, implies that yield is not concerned with the initiation of the deformation process, but only that the application of stress changes the rate of deformation until it equals imposed rate of change of strain. The Eyring approach is consistent with view that the deformation mechanisms are essentially present at zero stress, and are identical to those observed in linear viscoelastic measurements (site model analyses in Section 7.3.1). Here, a very low stress is applied merely to enable detection of the thermally activated process, without modification of the polymer structure. 

As in low molar mass systems crystal formation in a polymer melt starts with a nucleation step. Thermal fluctuations form in the melt embryos, i.e., particles with an enhanced inner order. If the size of an embryo surpasses a critical value it turns into the nucleus of a growing crj tal smaller embryos disappear again. It is possible to directly observe this process with an atomic force microscope, as is shown in Fig. 5.19 for a crystalhzing polyether (short name BA-C8, the material crystallizes slowly at room temperature). The encircled dot in the left-hand picture is a nucleus that subsequently develops into a single lamellar crystallite. 

Primary nuclei, forming when thermal fluctuations overcome a free energy barrier, appear randomly in space and in time, at a rate fluctuating around the momentary mean value, dictated for a given polymer by its thermomechanical history and crystallization conditions. Quiescent crystallization of homopolymers from the melt occurs usually in the form of spherulites growing radially from primary nuclei, as illustrated by... 

In practice, heterogeneous nudeation occurs in polymer crystallization. The multi-nudeation event was triggered in the crystal order parameter field based on the large density fluctuations driven by thermal perturbation. As can be witnessed in the... 

Samples were melt pressed in a vacuum laboratory hot press (Carver Press, Model C) at 160°C for 30 min. The molded films were then allowed to cool to room temperature under vacuum. A dual temperature chamber for the melt crystallization experiments consists of two large thermal chambers maintained at the melt temperature (Ti = 160°C) and the crystallization temperature (Ts = 81°C, 83°C, 86°C, 89°C, 92°C or 96°C). After 5-10 min at Ti, the copper sample cell was transferred rapidly ( 2 s) to the other chamber by means of a metal rod connected to a pneumatic device. A detailed description of the arrangement of the sample and of the two detectors used to measure WAXS and SAXS simultaneously has been provided previously [32]. Each polymer sample within the copper cell was 1.5 mm thick and 7 mm in diameter and was contained between two 25 im thick Kapton films. The actual sample temperature during crystallization (T2) and melting (Ti) was monitored by means of a thermocouple inserted into the sample cell. The crystallization temperature was usually reached 120 s after transfer without overshooting. Under isothermal conditions the fluctuations in the sample temperature are less than 0.5°C. Unless stated otherwise, all references to time are times elapsed after transferring the sample to the crystaUization chamber. 

Soft matter science is nowadays an acronym for an increasingly important class of materials, which encompasses polymers, liquid crystals, molecular assembhes building hierarchical structmes, and the whole area of colloidal sciences. Common to all of them is that fluctuations and thus the thermal energy T and the entropy play an important role. Soft then means that these materials are in a state of matter that are neither simple liquids nor hard solids of the type studied in hard condensed matter, hence sometimes soft matter firms also under the name complex fluids. 

In this section, we focus on the interplay between phase separations and phase ordering kinetics in mixtures of a flexible polymer and a liquid crystal (nematogen). When the system is thermally quenched from a stable isotropic phase into an unstable part of the biphasic region, the fluctuations of concentration and orientation take place and isotropic or nematic droplets appear with time [109, llOj. The instability of these systems is driven by the competition between phase separation and nematic ordering. Figure 2.22 shows the phase diagram of the polymer/liquid crystal mixture with Up = fir = 2 and a = 1.4. The solid curve refers to the binodal and the dotted line shows the first-order NIT. The dash-dotted line shows the spinodal. The arrows indicate temperature quenches from a stable isotropic phase... 

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