Random coil polymers

The crossover regime occurs at obstacle density C bs when the size of the random polymer coil becomes equal to the size of the pores, Rg =, obs-From Eqs. (46) and (47) in this regime follows... 

A liquid sphere can become elongated, if some conditions are fulfilled (see Section 11.3.2). As depicted, it obtains an orientation of about 45° to the direction of flow, and the liquid inside the particle rotates. Much the same holds for a (random) polymer coil it is also elongated, and its rotational motion now implies that the coil is compressed and extended (as indicated in the figure) periodically. It may be noted that this is a good example of the difference between the time scale of an event and the time that an experiment lasts. The time scale of compression/extension is simply 2/W (i.e., 1 ms if the shear rate is 2000 s-1), however long the shearing lasts. 

It has been demonstrated that the excimer emission intensity from chromophores incorporated into the vinyl polymer chain have been correlated with a change in the effective volume of random polymer coil in solution, and the volume of random polymer coil was correlated with viscosity, which is dependent on temperature. But a temperature change of a polymer solution does not always lead to expansion or contraction of the chain coil it can cause conformation change to a more or less packed polymer chain and to a more or less excimer forming conformation. Both of these structural changes in a polymer chain can affect the fluorescence, but each polymer needs to be considered individually. 

Fig. 7.10. Limiting slope from log-log plot of H - SALS profiles in a function of time when crystallizing EH064 at various crystallization temperatures. Note that the limiting slope for a Gaussian chain (random polymer coil) is 2...

Under a high electric field, DNA is no longer considered to move as a random-polymer coil, but moves with extended rod-like conformation. If DNA is completely extended, it moves in a straight fashion in the electric field direction, (x ) = L then... 

The onset of the steric exclusion force depends on the means of attaching the polymer chains to the substrates. For physically adsorbed polymer chains covering bodh surfaces, the steric exclusion force becomes detectable around 6Rg, where Rg is the unperturbed radius of gyration of the random polymer coil in solution (12), For terminally attached polymer chains, the repulsion commences around 12Rg (14), These values are approximate and depend on a number of factors including solvent quality, temperature, surface concentration and type of polymer chains attached to the surfaces. 

In many circumstances it is possible to extend the range of measurements with neutrons to cover more than this low Q limit, and then more detailed models of the structure must be evaluated. Debye [22] has derived a result for the scattering from a Gaussian distribution of polymer segments appropriate to a random polymer coil which is of the form ... 

In the simplest model for polymer coils, the chain is supposed to consist of n volume-less links of length / which can rotate freely in space. This model is then called the freely jointed chain model. Since each link can adopt any orientation, the polymer coil effectively executes a random walk, as sketched in Fig. 2.2. This is similar to the Brownian motion of microscopic particles suspended in a fluid (Section 1.4). The effect of the random walk statistics is that the chain coils back, and even crosses itself, many times, leading to a dense clumped up structure. The statistics of random walks were worked out for Brownian motion by Einstein (Section 1.4), and we can simply use the same result for random polymer coils. It turns out that the mean-square end-to-end distance is... 

Random polymer coils are often called Gaussian chains because the probability distribution function (for finding a segment in a given volume element) has a Gaussian shape. For linear Gaussian chains, the r.m.s. radius of gyration is... 

Next we consider the situation of a coil which is unperturbed in the hydro-dynamic sense of being effectively nondraining, yet having dimensions which are perturbed away from those under 0 conditions. As far as the hydrodynamics are concerned, a polymer coil can be expanded above its random flight dimensions and still be nondraining. In this case, what is needed is to correct the coil dimension parameters by multiplying with the coil expansion factor a, defined by Eq. (1.63). Under non-0 conditions (no subscript), = a(rg)Q therefore under these conditions we write... 

The reaction of a polymer in solution involves a considerably higher local concentration of functional groups than that indicated by the overall polymer concentration. Polymer molecules are generally present in solution as random-coil conformations. The concentration of functional groups is high within the polymer coils and zero outside [Alexandratos and Miller,... 

The elasticity of polymer coils is a well-known phenomenon and is involved in many important mechanical properties of bulk polymers. Stated briefly, it arises from a difference in conformational entropy between stretched and randomly jumbled chains. A statistical theory that counts the number of ways the two conformations can come about can be combined with the Boltzmann entropy equation (Equation (3.45)) to give an expression for the... 

From the picture presented in Fig. 7, one can expect that the sequential hydrophobization of a polymer coil should lead to a copolymer with a non-random sequence distribution. This is indeed the case. As an example, let us consider the average number fractions of blocks consisting of l neighboring amphiphilic monomers, /a( ), occurring in a copolymer chain. Some results are shown in Fig. 8 on a semilogarithmic scale. 

Viscosity. For homogeneous solution of polymers coiled at random, the viscosity uniformly is increasing with the chain length. 

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