Brownian motion micro

Network properties and microscopic structures of various epoxy resins cross-linked by phenolic novolacs were investigated by Suzuki et al.97 Positron annihilation spectroscopy (PAS) was utilized to characterize intermolecular spacing of networks and the results were compared to bulk polymer properties. The lifetimes (t3) and intensities (/3) of the active species (positronium ions) correspond to volume and number of holes which constitute the free volume in the network. Networks cured with flexible epoxies had more holes throughout the temperature range, and the space increased with temperature increases. Glass transition temperatures and thermal expansion coefficients (a) were calculated from plots of t3 versus temperature. The Tgs and thermal expansion coefficients obtained from PAS were lower titan those obtained from thermomechanical analysis. These differences were attributed to micro-Brownian motions determined by PAS versus macroscopic polymer properties determined by thermomechanical analysis. 

Far below the glass transition temperature (T see Sect. 2.3.4.3) the macro-Brownian motions are frozen in completely, and most of the micro-Brownian motions are frozen in as well ( glassy state ). Near Tg, the micro-Brownian motions set in and become stronger with increasing temperature. The material softens. Finally, upon further raise of temperature, the macro-Brownian motions set in as well, and the polymer can be deformed by applying an external force. 

Softening as a result of micro-Brownian motion occurs in amorphous and crystalline polymers, even if they are crosslinked. However, there are characteristic differences in the temperature-dependence of mechanical properties like hardness, elastic modulus, or mechanic strength when different classes of polymers change into the molten state. In amorphous, non-crosslinked polymers, raise of temperature to values above results in a decrease of viscosity until the material starts to flow. Parallel to this softening the elastic modulus and the strength decrease (see Fig. 1.9). 

When polymer melts, rubbers, or elastomers are cooled down below Tg, they may freeze to glasses (noncrystalline amorphous phases). The rotations motions of the chain segments (micro-Brownian motions) are almost stopped now, and the transparent materials become stiff and (in most cases) brittle. 

Because of the kinetic energy present in the molecule, amorphous flexible polymer chains are usually in constant motion at ordinary temperatures. The extent of this wiggling-like segmental motion decreases as the temperature is lowered in this reversible process. The temperature at which this segmental or micro-Brownian motion of amorphous polymers becomes significant as the temperature is increased is called the glass transition temperature, Te The term free volume is used to describe the total vplume occupied by the holes. 

The molecular movements of the chain determine the elastic range of polymers. In this unique state of rubber like elasticity there is freedom of the micro-Brownian motion of the chain units and a high relaxation time for the macro-Brownian motion of the entire chain. This state can be described as a liquid with a fixed structure U6). 

High-resolution NMR in solution requires the sample to be soluble in a solvent such that the various nuclear spin interactions can be averaged or removed by molecular micro-Brownian motions. Unfortunately, elastomers used in various applications are normally crosslinked materials and therefore not soluble in any solvent. Thus, solid state NMR with magic angle-spinning technique has been used with great success in the study of cured elastomers. However, this technique demands extended instrument facilities and expertise. 

A secondary stereocomplex gel with the ratio [iso-PMMA]/[synd-PMMA] = 1/1 obtained from o-xylene solution showed an endothermic peak at 110 °C which was attributed to the melting point of the stereocomplex. The degree of crystallization was about 5-6%. Since this gel contained over 80% solvent, micro-Brownian motions of PMMA chains in the amorphous region were relatively unhindered. When the PMMA gel was cooled rapidly after melting above its Tm (i.e. above 145°C), first the loss modulus (c") changed relative to the viscosity of the system whereas the storage modulus began to increase after some time. This result confirms the assumption that first the polymer chains cannot be cross-linked but are weakly associated with one other, and then a... 

When matrix polymerization of methyl methacrylate monomer was performed in the presence of iso-PMMA or of the stereocomplex ([iso-PMMA]/ [synd-PMMA] = 1/1), the tan 6 peaks of the a-process (caused by the micro-Brownian motions of main chain) and the / -process (caused by the motions of the ester side chains of PMMA) shifted to temperature ranges which were higher by 5-10°C and 30-40 °C, respectively, as compared with synd-PMMA312. From these results, Tanzawa et al. concluded that the stereospecific association drastically restricted the motion of the ester side chains of the two stereoregular PMMAs. In addition, the mutual interlocking of the side chains of PMMA also hindered, to a certain extent, the motion of the main chains of PMMA. Furthermore, they studied the matrix polymerization of methyl acrylate (MA) and ethyl acrylate (EA) in the presence of stereoregular PMMA and found ... 

The majority of the different chemical and physical properties, as well as the morphology of microemulsions, is determined mostly by the micro-Brownian motions of its components. Such motions cover a very wide spectrum of relaxation times ranging from tens of seconds to a few picoseconds. Given the complexity of the chemical makeup of microemulsions, there are many various kinetic units in the system. Depending on their nature, the dynamic processes in the microemulsions can be classified into three types ... 

The theoretical aspects of the micro-Brownian motion of polymer chains in solution in connection with problems of the PL are dealt with in Sect. 5. They include the problems of the shape and width of relaxation spectra and the most probable relaxati6n times manifested in the motion of a given labelled chain element, active in the PL, and the problems of the superposition of various types of motions and the anisotropy of local relaxation properties etc. 

The value of in Eq. (1.2.1) is the mean square cosine of the rotation angle 6 of the emitting oscillator during time /, Tf the average lifetime of the oscillator in the excited state with an exponential decay and P the value of polarization measured experimentally under steady-state irradiation. The value of Tf represents the characteristic time scale with which the times of the micro-Brownian motion of the oscillator of a lumines nt molecule or a luminescent group in the maaromolecule are compared. 

The analysis of experimental data on the micro-Brownian motion in polymer chains and the theory of relaxation phenomena in polymers (see Sect. 5) show that the Brownian motion of an oscillator in a luminescent marker covalently bonded to the chain obeys a more complex time law than Eq. (1.2.3). According to the theory of the relaxation processes, for a non-inertial physical system, the decay of will described by a spectrum of relaxation times (or, more precisely,... 

Only when some assumptions (sometimes relatively arbitrary and not unique) are made about additional torsional-vibrational or other motions superimposed on the segmental micro-Brownian motion of the main chain, is it possible to obtain a faster decrease in L(j) at t or in CP2(cos 6)) at t ->... 

In the PL of macromolecules, the same or similar relaxation times and forms of bcal micro-Brownian motions occur as in local processes determining dielectric, mechanical and nuclear magnetic relaxation. 

The first and most rigorous theory on the viscoelasticity was developed by Kirkwood (25). In this theory it is considered that the chain elements counteract the hydrodynamic torques through their micro-brownian motion (26). Then the statistical orientation of the macromolecule in the velocity field of the solvent contributes terms linear as well as non-linear in the rate of shear to the stress and thus to the Newtonian part of the intrinsic viscosity. This nonlinear term exhibits a phase lag when a sinusoidal hydrodynamical force is applied. 

This shows that this polymer has no micro-Brownian motion of the Si-C backbone. 

Figure 19 shows plots of the Si chemical shifts and half width of the 2 Si NMR signals of PMPhSM at —37 to 65 C. The Tg of this polymer is about 20° C obtained by storage moduli and loss moduli. The broad signal below the Tg implies conformational distribution along the Si-C backbone and a micro-Brownian motion of the Si C backbone occurs above Tg. This motion leads to a decrease in the half width of the signal. 

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