Of flexible polymers

In all of these derivations concerning rigid bodies, no other walls are considered except the particle surfaces. Before we turn to the question of the intrinsic viscosity of flexible polymers, let us consider the relationship between the viscosity of a fluid and the geometry and dimensions of the container in which it is measured. 

Taking the attitude described in item (5) toward the previously developed equations for [r ] is an important step. Wliat this enables us to do is write a general expression for [r ] in solutions of flexible polymers ... 

It is somewhat difficult conceptually to explain the recoverable high elasticity of these materials in terms of flexible polymer chains cross-linked into an open network structure as commonly envisaged for conventionally vulcanised rubbers. It is probably better to consider the deformation behaviour on a macro, rather than molecular, scale. One such model would envisage a three-dimensional mesh of polypropylene with elastomeric domains embedded within. On application of a stress both the open network of the hard phase and the elastomeric domains will be capable of deformation. On release of the stress, the cross-linked rubbery domains will try to recover their original shape and hence result in recovery from deformation of the blended object. 

These models are designed to reproduce the random movement of flexible polymer chains in a solvent or melt in a more or less realistic way. Simulational results which reproduce in simple cases the so-called Rouse [49] or Zimm [50] dynamics, depending on whether hydrodynamic interactions in the system are neglected or not, appear appropriate for studying diffusion, relaxation, and transport properties in general. In all dynamic models the monomers perform small displacements per unit time while the connectivity of the chains is preserved during the simulation. 

J. H. van Vliet, G. ten Brinke. Orientation and shape of flexible polymers in a slit. J Chem Phys 95 1436-1441, 1990. 

The properties of flexible polymer chains moving in porous structures, that is, in structures with geometric constraints such as tubes or slits, apart from their Tclevance for various applications such as filtration, gel permeation chromatography, oil recovery, etc., pose an exciting problem of statistical... 

The non-free draining character of flexible polymer chains was considered in the Zimm model [48], In this model, the effect of hydrodynamic interaction at the location of bead i is taken into account by an additional fluid velocity term vj ... 

Diffusion of flexible macromolecules in solutions and gel media has also been studied extensively [35,97]. The Zimm model for diffusion of flexible chains in polymer melts predicts that the diffusion coefficient of a flexible polymer in solution depends on polymer length to the 1/2 power, D N. This theoretical result has also been confirmed by experimental data [97,122]. The reptation theory for diffusion of flexible polymers in highly restricted environments predicts a dependence D [97,122,127]. Results of various... 

MC simulations and semianalytical theories for diffusion of flexible polymers in random porous media, which have been summarized [35], indicate that the diffusion coefficient in random three-dimensional media follows the Rouse behavior (D N dependence) at short times, and approaches the reptation limit (D dependence) for long times. By contrast, the diffusion coefficient follows the reptation limit for a highly ordered media made from infinitely long rectangular rods connected at right angles in three-dimensional space (Uke a 3D grid). 

Mapping Atomistically Detailed Models of Flexible Polymer Chains in Melts to Coarse-Grained Lattice Descriptions ... 

A preliminary analysis of the features of thermotropic mesophases of flexible polymers we just described, leads us to envisage a path of polymer crystallization different from chain-folded, fold-preserving crystallization in-... 

In an ensemble of flexible polymer chains, the instantaneous separation of two segments i and j varies from one molecule to another. Ensemble averages such as required in Eq. 2 are obtained by specifying W(r-jj), the probability that segments i and j are separated by ry. In an elastomeric rubber which is not so highly swollen that excluded volume interactions become important, and which is not too greatly deformed, W(r- j) takes a particularly simple form... 

A change in the environment of a protein molecule, e.g. adsorption from aqueous solution onto a sorbent surface, may lead to a partial breakdown of its ordered structure, resulting in an increase of conformational entropy. This is a fundamental difference between protein adsorption and the adsorption of flexible polymers, for which attachment to a surface implies a loss of conformational entropy. 

Nonlinear Electro-optic and Dielectric Properties of Flexible Polymers... 

We have shown in this paper the relationships between the fundamental electrical parameters, such as the dipole moment, polarizability and hyperpolarizability, and the conformations of flexible polymers which are manifested in a number of their electrooptic and dielectric properties. These include the Kerr effect, dielectric polarization and saturation, electric field induced light scattering and second harmonic generation. Our experimental and theoretical studies of the Kerr effect show that it is very useful for the characterization of polymer microstructure. Our theoretical studies of the NLDE, EFLS and EFSHG also show that these effects are potentially useful, but there are very few experimental results reported in the literature with which to test the calculations. More experimental studies are needed to further our understanding of the nonlinear electrooptic and dielectric properties of flexible polymers. 

Simulation methods have been proved to be useful in the study of many different molecular systems, in particular in the case of flexible polymers chains [ 14]. According to the variety of structures and the theoretical difficulties inherent to branched structures, simulation work is a very powerful tool in the study of this type of polymer, and can be applied to the general problems outHned above. Sometimes, this utility is manifested even for behaviors which can be explained with simple theoretical treatments in the case of linear chains. Thus, the description of the theta state of a star chain cannot be performed through the use of the simple Gaussian model. The adequate simulation model and method depend strongly on the particular problem investigated. Some cases require a realistic representation of the atoms in the molecular models [10]. Other cases, however, only require simplified coarse-grained models, where some real mon-... 

The first ingredient in any theory for the rheology of a complex fluid is the expression for the stress in terms of the microscopic structure variables. We derive an expression for the stress-tensor here from the principle of virtual work. In the case of flexible polymers the total stress arises to a good approximation from the entropy of the chain paths. At equilibrium the polymer paths are random walks - of maximal entropy. A deformation induces preferred orientation of the steps of the walks, which are therefore no longer random - the entropy has decreased and the free energy density/increased. So... 

In the second part of this Chapter the thickness of the organic layer under discussion is slightly increased and a closer look at recent developments of more complex surface-bonded systems involving polymers is outlined. Despite the introduction of flexible polymer chains, the surface coating should still be defined and uncontrolled heterogeneities minimized. Here, especially, polymer brush-type layers where self-assembled monolayers (SAMs) are used as two-dimensional template systems for the preparation of well-defined surface coatings will be subject of a more detailed discussion. 

Another very interesting class of crosslinked polyelectrolytes are the so-called superabsorbents. They predominantly consist of crosslinked and (partially) neutralized poly(acrylic acid) and, hence, represent a network of flexible polymer chains that carry dissociated, ionic groups. Due to this structure they can function as water-swellable gels. Although they are hard, sandy powders in a dry... 

Table 1. Critical dextran concentrations (kg m 3) determined from the onset of rapid transport of flexible polymers (from ref.S1).

With increasing polymer concentration, we may expect that the polymer global motion changes from the fuzzy cylinder model mechanism to the repta-tion model mechanism. The onset of the crossover should depend on the degree in which the lateral motion of a polymer chain is suppressed by entanglement with its surrounding chains, but it is difficult to estimate this degree. There are some disputes over it in the case of flexible polymers [20]. 

The equilibrium structure is considered of flexible polymer chains within the RIS model. This model is solved by an irreducible tensor method which is somewhat different from, and simpler than, the approach of Flory and others. The results are used to compute the light scattering intensities from dilute solutions of flexible polymer chains, and the angle dependence is found... 

An approximate analytical solution is presented for the RIS model of flexible polymer configurations. The method is applied to calculate and . 

It is suggested by several equations describing the solution behavior of flexible polymers in good solvents that the second and third virial coefficients of the concentration dependence have a common parameter dependence 12-14). This behavior may be attributed to interchain entanglements for some polymers. In contrast, rigid rods can show completely linear concentration dependence in moderately dilute solution. Here the third virial coefficient is either negligibly small, or it is non-existent—in which case no relation exists between the second and third coefficient. Viscometry of some polyisocyanide solutions shows time-dependent transformations, reflected in pronounced changeovers from parabolic to linear concentration dependencies, and it would be of interest to define the transformations, and to detail their physical descriptions. 

Upon cooling of solutions of long-chain polymers it may happen that only parts of the chain eventually crystallize together with parts of other polymer chains. When a number of such small crystallites are formed they operate as knots in a network of flexible polymer chains in solution and one obtains a gel. Processing of such gels into strong fibres and films is applied commercially and has been reviewed [13,14]. 

Daoud M, Cotton JP, Famoux B, Jannink G, Sarma G, Benoit H, Dupressix R, Picot C, De-Gennes PG (1975) Solutions of flexible polymers. Neutron experiments and interpretation Macromolecules 6 804... 

ASTM D2137, 1994 (2000). Brittleness point of flexible polymers and coated fabrics. 

As we have seen, the phase behaviour of block copolymers consisting of flexible polymer coils is remarkably rich. If one of the blocks is rigid, the copolymer would be expected to exhibit even more complex phase behaviour. For example, the rigid block could be mesogenic. This leads to the possibility of self-assembly of structures consisting of domains of liquid crystalline material within a microphase-separated block copolymer superstructure. Diblock copo-... 

The shape of flexible polymer molecule in the vicinity of the surface is greatly distorted from the average shape in solution. Adsorbed polymer molecules are attached to the surface by stretches of segments at the surface alternating with loops out of the surface (Fig. 10.7). 

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