Relaxation chain

Thus, fracture occurs by first straining the chains to a critical draw ratio X and storing mechanical energy G (X — 1). The chains relax by Rouse retraction and disentangle if the energy released is sufficient to relax them to the critically connected state corresponding to the percolation threshold. Since Xc (M/Mc) /, we expect the molecular weight dependence of fracture to behave approximately as... 

Finally, we want to describe two examples of those isolated polymer chains in a sea of solvent molecules. Polymer chains relax considerably faster in a low-molecular-weight solvent than in melts or glasses. Yet it is still almost impossible to study the conformational relaxation of a polymer chain in solvent using atomistic simulations. However, in many cases it is not the polymer dynamics that is of interest but the structure and dynamics of the solvent around the chain. Often, the first and maybe second solvation shells dominate the solvation. Two recent examples of aqueous and non-aqueous polymer solutions should illustrate this poly(ethylene oxide) (PEO) [31]... 

Clearly, both the pivot and the slithering snake algorithms are incapable of reproducing true chain dynamics at molecular basis, covering the time range of typical chain relaxation times. Therefore, in the following we focus on two alternative methods, broadly used at present to this end. 

Fig. 12. Molecular weight dependences of the normalized chain relaxation time, tJTs, for linear polymers ( ), branched fractions ( ), and branched feed polymer (+). (Reproduced with permission from [88]. Copyright 2001 American Chemical Society.)...

The MW dependences of the normalized chain relaxation times in melts of linear and branched samples are compared in Fig. 12. Both can be represented by scaling power laws, but with remarkably different scaling exponents. For the melts of linear chains, the exponent 3.39 is observed close to the typical value of 3.4 for such systems. In contrast, for the fractions of the branched polymer, the exponent is considerably lower (2.61). It is interesting to note that the value of the normalized chain relaxation time for the feed polymer with the broad M WD fits nicely into the data for the fractions with narrow MWDs. This seems to indicate that conclusions can also be drawn from a series of hyperbranched polymers with broad MWDs. 

Another approach, neglecting the details of the chemical structure and concentrating on the universal elements of chain relaxation, is based on dynamic scaling considerations [4, 11], In particular in polymer solutions, this approach offers an elegant tool to specify the general trends of polymer dynamics, although it suffers from the lack of a molecular interpretation. 

Thus, with decreasing Q a crossover from the single-chain to the collective many-chain relaxation occurs at Q = 1/1 (c) (see Fig. 58a). 

Fig. 60. Crossover from single-chain to many-chain relaxation at T = 343 K. Lineshape analysis for PDMS/d-benzene at c = 5 and 18% double logarithmic plot of — ln/S(Q,t)/S(Q,0) vs. t/s. (Reprinted with permission from [116]. Copyright 1982 J. Wiley and Sons, Inc., New York)...

Under good solvent conditions the crossover from single-chain relaxation to collective diffusion (many-chain behavior) can be observed by variation of the Q-value... 

The crossover from the single to the many-chain relaxation (Q(Q) Q2), which is expected to follow at further decreasing Q-values, has not yet been detected by the NSE technique... 

Some TICT-forming fluorescent probes containing the / j - /V. /V - cl i a I k I a m i n o benzylidene malononitrile motif (usually related to 30 in Fig. 11) have been applied to monitor and quantify polymerization reaction, crosslinking, chain relaxation,... 

Even at their best, the models are able to predict only macroscopic properties of the films, yielding no information on microscopic parameters that may affect resist performance. It is highly probable that spin casting induces some structure or preferential chain orientation into the films, or causes secondary effects such as the aggregation observed by Law. These effects are barely addressed in the currently available literature. However, some earlier works (3.17-191 on solvent (static) cast films have investigated the molecular orientation of polymer chains as well as chain relaxation due to thermal annealing. 

Brostow W. The Chain Relaxation Capability. Ch. 5. In performance of Plastics. Ed. W. Brostow, Hanser, Munich-Cincinnati, 2000. 

Molecular rotors allow us to study changes in free volume of polymers as a function of polymerization reaction parameters, molecular weight, stereoregularity, crosslinking, polymer chain relaxation and flexibility. Application to monitoring of polymerization reactions is illustrated in Box 8.1. 

The dynamical history of stress-relaxation in a star-linear blend begins life in just the same way as a star-star blend,because when t r gp the linear chain relaxation is dominated by pathlength fluctuation and behaves as a two-arm star with M =Mii /2. So very early Rouse fluctuation (Eq. 25) crosses over to activated fluctuation in self-consistent potentials. These are calculated via the coordinate transformation used in the star-star case above. For example, the effective potential for the star component in this regime is... 

The polycarbonate membranes are stretch-oriented during fabrication in order to improve their mechanical properties. If the membrane is subsequently heated above its glass-transition temperature ( 150°C), the polymer chains relax to their unstretched conformation and the membrane shrinks. This shrinking of the membrane around the Au nanowires in the pores causes the junction between the nanowire and the pore wall to be sealed. This is illustrated in Fig. 5, which shows voltammograms for tri-methylaminomethylferrocene (TMAFc+) before (Fig. 5A) and after (Fig. 

S. Jun, J. Bechhoefer, andB.-Y. Ha, Diffusion-limited loop formation of semiflexible polymers Kramers theory and the intertwined time scales of chain relaxation and closing. Europhys. Lett. 64, 420-426 (2003). 

Further note that for t=0 Eq. 3.24 does not resemble the Debye function but yields its high Q-limiting behaviour i.e. it is only valid for QR >1. In that regime the form of Dr immediately reveals that the intra-chain relaxation increases in contrast to normal diffusion ocQ, Finally, Fig. 3.2 illustrates the time development of the structure factor. 

Note that another origin of the slowing down of the chain relaxation compared to the Rouse prediction could be a reduction of the weights of the higher modes, which in the Rouse model are proportional top (see Eq. 3.19). 

Fig. 6.25 Relaxation rates as function of Q in semidilute PDMS/toluene solutions. A collective concentration fluctuation seen in normal contrast, C single chain motion as seen in zero average contrast. B Zimm regime of local chain relaxations, equal in both contrasts. (Reprinted with permission from [325]. Copyright 1991 EDP Sciences)...

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