Brownian motion of polymers

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. 

In an excellent review article, Tirrell [2] summarized and discussed most theoretical and experimental contributions made up to 1984 to polymer self-diffusion in concentrated solutions and melts. Although his conclusion seemed to lean toward the reptation theory, the data then available were apparently not sufficient to support it with sheer certainty. Over the past few years further data on self-diffusion and tracer diffusion coefficients (see Section 1.3 for the latter) have become available and various ideas for interpreting them have been set out. Nonetheless, there is yet no established agreement as to the long timescale Brownian motion of polymer chains in concentrated systems. Some prefer reptation and others advocate essentially isotropic motion. Unfortunately, we are unable to see the chain motion directly. In what follows, we review current challenges to this controversial problem by referring to the experimental data which the author believes are of basic importance. 

The Brownian motion of polymers can be experimentally studied by dynamic light scattering. By measuring the time correlation of the... 

We now neglect the inertia term (the acceleration term) in (9.1) as in the conventional treatment of the Brownian motion of polymer chains [24,25], solve it in the form... 

The coupled Brownian motion of polymer segments can be resolved into a linear combination of the motion of Rouse modes, essentially a Fourier transformation in position along the chain. The Rouse modes behave as independent, overdamped, harmonic oscillators. Hydrodynamic interactions arise from the flow field accompanying one segment s motion creating flow at other segments. Increase of concentration leads to a screening of hydrodynamic interactions. 

It has already been mentioned that polymer melts are non-Newtonian and are in fact under normal circumstances pseudoplastic. This appears to arise from the elastic nature of the melt which will be touched on only briefly here. In essence, under shear, polymers tend to be oriented. At low shear rates Brownian motion of the segments occurs so polymers can coil up at a faster rate than they are oriented and to some extent disentangled. At high shear rates such re-entangling rates are slower than the orientation rates and the polymer is hence apparently less viscous. 

Diffusion of small molecular penetrants in polymers often assumes Fickian characteristics at temperatures above Tg of the system. As such, classical diffusion theory is sufficient for describing the mass transport, and a mutual diffusion coefficient can be determined unambiguously by sorption and permeation methods. For a penetrant molecule of a size comparable to that of the monomeric unit of a polymer, diffusion requires cooperative movement of several monomeric units. The mobility of the polymer chains thus controls the rate of diffusion, and factors affecting the chain mobility will also influence the diffusion coefficient. The key factors here are temperature and concentration. Increasing temperature enhances the Brownian motion of the polymer segments the effect is to weaken the interaction between chains and thus increase the interchain distance. A similar effect can be expected upon the addition of a small molecular penetrant. 

Although many different processes can control the observed swelling kinetics, in most cases the rate at which the network expands in response to the penetration of the solvent is rate-controlling. This response can be dominated by either diffu-sional or relaxational processes. The random Brownian motion of solvent molecules and polymer chains down their chemical potential gradients causes diffusion of the solvent into the polymer and simultaneous migration of the polymer chains into the solvent. This is a mutual diffusion process, involving motion of both the polymer chains and solvent. Thus the observed mutual diffusion coefficient for this process is a property of both the polymer and the solvent. The relaxational processes are related to the response of the polymer to the stresses imposed upon it by the invading solvent molecules. This relaxation rate can be related to the viscoelastic properties of the dry polymer and the plasticization efficiency of the solvent [128,129],... 

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. 

Bitsanis et al. [122,123] simulated Brownian motion of rodlike polymers over the concentration range 5 < LV < 150, where L and c are the length and number concentration of the rod, respectively, with the intermolecular potential u given by... 

Iwata,L, Kurata,M. Brownian motion of lattice-model polymer chains. J. Chem. Phys. 50,4008 4013 (1969). 

Bird,R.B., Warner,H.R.,Jr., Evans,D.G Kinetic theory and rheology of dumbbell suspensions with brownian motion. Advan. Polymer ScL 8,1-90 (1971). 

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). 

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... 

The basic models consider well-defined star-branched polymers. De Gennes [11] imagined in 1975 a simple relaxation mechanism of a branch based on the Brownian motion of an arm of a star-branched molecule in a network of fixed obstacles (Figure 13). From statistical considerations, the time necessary for a branch to renew its configuration is ... 

The evolution of the experimental anisotropy as a function of the temperature is shown in Fig. 8. As expected, the decay rate increases as the temperature increases. For the highest temperature (t > 50 °C), it can be noticed that the anisotropy decays from a value close to the fundamental anisotropy of DMA to almost zero in the time window of the experiment (about 60 ns). This means that the initial orientation of a backbone segment is almost completely lost within this time. This possibiUty to directly check the amplitude of motions associated with the involved relaxation is a very useful advantage of FAD. In particular, it indicates that in the temperature range 50 °C 80 °C, we sample continuously and almost completely the elementary brownian motion in polymer melts. Processes too fast to be observed by this technique involve only very small angles of rotation and cannot be associated with backbone rearrangements. On the other hand, the processes too slow to be sampled concern only a very low residual orientational correlation, i.e. they are important only on a scale much larger than the size of conformational jumps. 

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,... 

The changes have been used to provide information about the enviromnent of the fluorescent probe and to follow changes in conformation of the macromolecule. In other work the study of the fluorescence polarization properties of the attached probe under steady state illumination and the application of Perrin s equation enable calcu-latnn of the rotary Brownian motion of the polymer. This technique has been extended by Jablonski and Wahl to the use of time-resolved fluorescence polarization measurements to calculate rotational relaxation times of molecules These experiments are discussed fiilly in the fdlowing section of this review. 

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. 

---