Polymer coil size

The function P(6) is size dependent and can be related to the polymer coil size by the well-known Debye equation... 

Fig. C9.3 The dependence a x) given by Equation (9.7) for different values of y from top to bottom, the curves correspond to the following values of y 10, 1, 0.1, 1/60, 0.01, 0.001, 0.0001. Here a is the swelling parameter, that is, the ratio of the actual polymer coil size to ideal coil size a < 1 corresponds to chain collapse, or formation of a globule. Parameters x and y are defined such that x is controlled by the solvent quality and chain length (x while y is determined by the chain stiffness (y C/ ) small values...

The absorption of light by the diphenylanthracene was found to result in efficient intracoil sensitization by fluorescene. The quantum efficiency of this process was determined to be 0.4 in methanol and 0.8 in water. This increase corresponds to a decrease in polymer coil size in water. Analysis of the fluorescence decay also demonstrates that the intracoil energy transfer is essentially a static process and that aggregation can result in nonexponential fluorescence decay that is interpreted as a dynamic equilibrium that takes place between diphenylanthracene and a nonfluorescent dimer state... 

Coil Expansion in Good Solvent Flory Theory of Polymer Coil Size... 

The above result is remarkably useful and universal. It is valid for any ideal polymer system provided that the characteristic length-scale A of the concentration profile c(r) is larger than the chain persistence I but is shorter than the polymer coil size R = J ee = I< A< R. 

As a simple application of eqn [74] consider a solid colloidal particle of radius Rj immersed in an ideal solution of long overlapping polymer chains (concentration of units c) assuming that polymer coil size R > R and cb Rs 3> 1 (see eqn [75]). The monomer-particle interactions are assumed to be purely repulsive (sterical). The minimal work W required to move the particle into the solution is related to the probability that a volume Vs = R in a solution is free from polymer segments. W is equal to the excess free energy due to an inhomogeneous distribution of chain segments induced by the particle ... 

The polymer-induced interaction between the walls is therefore repulsive. The repulsion force per unit area (the excess pressure) is f k T/DA, that is, the force shows a power-law (rather than exponential) decay. An analysis of the finite chain length effect shows that this decay is cut off at D 0.5N b comparable with the polymer coil size. Note that the long-range energy, eqn [122], is valid whatever the monomer/ wall interactions are, that is, both for repulsive and attractive walls (and in the case when one surface is repulsive and another attractive). 

The factor a is 1 for the unperturbed coil defined in this way, and is larger (or smaller) when a polymer molecule is expanded (or compressed) due to polymer-solvent interactions. Thus, for an idealized freely jointed chain in theta solvent, we have = nl, and the corresponding mean square radius of gyration = nf-/G. When one accounts for the steric effects that prevent distant chain segments from overlapping (excluded volume effect), the dependence of (r ) is predicted to be (closer to experimental observation), rather than [Eq. (5)]. This polymer coil size is much larger than that based on polymer density, and hence markedly influences the viscosity behavior of 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... 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

Polymerizations Above Tg. Let the polymerization begin in pure monomer. As the concentration of polymer chains increases initially one observes a relatively small increase in the termination rate constant. This is related to the effect of polymer concentration on coil size. A reduction in coil size increases the probability of finding a chain end near the surface and hence causes an increase in k-. Soon thereafter at conversions 15-20 polymer chains begin to entangle causing a dramatic reduction in radical chain translational mobility giving a rapid drop in k-j. ... 

Mixed solvents are generally unsatisfactory for use in the determination of polymer molecular weights owing to the likelihood of selective absorption of one of the solvent components by the polymer coil. The excess of polarizabilit f of the polymer particle (polymer plus occluded solvent) is not then equal to the difference between the polarizabilities of the polymer and the solvent mixture. For this reason the refractive increment dn/dc which would be required for calculation of K, or of i7, cannot be assumed to equal the observed change in refractive index of the medium as a whole when polymer is added to it, unless the refractive indexes of the solvent components happen to be the same. The size Vmay, however, be measured in a mixed solvent, since only the dissymmetry ratio is required for this purpose. 

A polymer coil does not only possess a structure on the atomistic scale of a few A, corresponding to the length of covalent bonds and interatomic distances characteristic of macromolecules are coils that more or less, obey Gaussian statistics and have a diameter of the order of hundreds of A (Fig. 1.2) [17]. Structures of intermediate length scales also occur e. g., characterized by the persistence length. For a simulation of a polymer melt, one should consider a box that contains many such chains that interpenetrate each other, i. e., a box with a linear dimension of several hundred A or more, in order to ensure that no artefacts occur attributable to the finite size of the simulation box or the periodic boundary conditions at the surfaces of the box. This ne-... 

The bond fluctuation model not only provides a good description of the diffusion of polymer chains as a whole, but also the internal dynamics of chains on length scales in between the coil size and the length of effective bonds. This is seen from an analysis of the normalized intermediate coherent scattering function S(q,t)/S(q,0) of single chains ... 

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

Since microgels are intramolecularly crosslinked macromolecules of colloidal dimensions, it is necessary for their synthesis to control the size of the growing crosslinked molecules. This can be achieved by carrying out polymerization and crosslinking in a restricted volume, i.e. that of a micelle or of a polymer coil. Thus, two general methods of microgel synthesis are available (1) emulsion polymerization, and (2) solution polymerization. 

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