Relaxation in polymer solution

The use of NMR relaxation in polymer solutions is well known (115). This is an excellent technique to study polymer chain dynamics (116), polymer/polymer, polymer/solvent, polymer/additive interactions (117), and phase transitions (118). 

Adachi, K. (1997), Dielectric relaxation in polymer solutions, in Dielectric Spectroscopy of Polymeric Materials—Fundamental and Applications,P. and Fitzgerald, J. I, eds., ACS, Washington, DC, pp. 261-282. 

PhilippofF, W. (1965). In Relaxation in Polymer Solutions and Gels in Physical Acounstics, Vol. II, Part B, W.P. Mason, ed.. New York Academic Press. 

R Stepanek, Z. Tuzar, P. Kadlec, and J. Kriz. A dynamic light scattering study of fast relaxations in polymer solutions. Macromolecules, 40 (2007), 2165-2171. 

R. Granek. Stress relaxation in polymer melts and solutions Bridging between the breathing and reptation regimes. Macromolecules 2<5 5370-5371, 1995. 

The earliest and simplest approach in this direction starts from Langevin equations with solutions comprising a spectrum of relaxation modes [1-4], Special features are the incorporation of entropic forces (Rouse model, [6]) which relax fluctuations of reduced entropy, and of hydrodynamic interactions (Zimm model, [7]) which couple segmental motions via long-range backflow fields in polymer solutions, and the inclusion of topological constraints or entanglements (reptation or tube model, [8-10]) which are mutually imposed within a dense ensemble of chains. 

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. 

The use of photon correlation spectroscopy to study the dynamics of concentration fluctuations in polymer solutions and gels is now well established. In bulk polymers near the glass transition there will be slowly relaxing fluctuations in density and optical anisotropy which can also be studied by this technique. In this article we review the development of the field of photon correlation spectroscopy from bulk polymers. The theory of dynamic light scattering from pure liquids is presented and applied to polymers. The important experimented considerations involved in the collection and analysis of this type of data are discussed. Most of the article focuses on the dynamics of fluctuations near the glass transition in polymers. All the published work in this area is reviewed and the results are critically discussed. The current state of the field is summarized and many suggestions for further work are presented. 

C.J. Farrell, A. Keller, M.J. Miles, and D.P. Pope, Conformational relaxation time in polymer solutions by elongational flow experiments 1. Determination of exten-sional relaxation time and its molecular weight dependence, Polymer, 21,1292 (1980). 

For a polymer solution, p ss 10 2 Ps, p k, 1 g/cm3, and the size of macro-molecular coil is a k, 10-5 cm, which allow us to estimate the relaxation time r 10 1° s. Processes with relaxation times so small are not essential when compared to other relaxation processes in polymer solutions. 

In the simplest case, at N = 1, the considered subchain model of a macromolecule reduces to the dumbbell model consisting of two Brownian particles connected with an elastic force. It can be called relaxator as well. The re-laxator is the simplest model of a macromolecule. Moreover, the dynamics of a macromolecule in normal co-ordinates is equivalent to the dynamics of a set of independent relaxators with various coefficients of elasticity and internal viscosity. In this way, one can consider a dilute solution of polymer as a suspension of independent relaxators which can be considered here to be identical for simplicity. The latter model is especially convenient for the qualitative analysis of the effects in polymer solutions under motion. 

Most studies of magnetic relaxation in polymers have dealt with solid or melted polymers (73)] however, Odajima (20) has studied proton relaxation in solutions of polystyrene and polyisobutylene. It is desirable to extend and refine such measurements. In concentrated solution, some insight into the motional effects of polymer-solvent interactions should be obtainable and if, despite low sensitivity, reliable 7 values can be obtained for polymers in dilute solutions, valuable information concerning the detailed motional behavior of isolated polymer molecules may be provided. 

The theoretical analysis of the relationship between small-scale relaxation processes in polymers PL reveals just these processes) and the intra- or intermolecular inter-actions shows that these processes are sensitive to various changes in the number (probability of formation) of intra- or interchain contacts in polymer solutions. The experimental data reveal that the intramolecular mobility (IMM) of the polymer in solution is highly susceptible to various conformational transformations of macro-molecules and to changes in the intermolecular interactions in complex multicom-... 

Three emission bands (a, p and y in the order of decreasing energy) are observed in CH2CI2 solution and are found to be the emission from the excited state of 1, from the excited state of a solute-solvent complex and from a relaxed twisted excited state of the solute-solvent complex, respectively. Model compound studies show that squaraine forms strong solute-solvent complexes with alcoholic solvent molecules. Analogous complexation process between 1 and the OH groups in PVF is also shown to occur. A model for the stabilization of particles of 1 in polymer solution is put forward where we propose that the stabilization mechanism is a steric effect achieved by adsorption of PVF macromolecules onto particles of 1 via the formation of the PVF 1 complex. 

Here we report preliminary results on the multiple fluorescence emission of 1 and 2. From structure-property relationships, solvent effect and temperature effect studies, we are able to show that the multiple emission is from the emission of free squaraine in solution, the emission of the solute-solvent complex and the emission of a twisted relaxed excited state. Further solvent effect study using 2 as a model shows that squaraine forms strong solute-solvent complexes with alcoholic solvent molecules. Analogous complex-ation process is also detected between 1 and the hydroxy groups on the macromolecular chains of poly(vinyl formal). The Important role of this complexation process on the stabilization mechanism of particles of 1 in polymer solution is discussed. 

Spin relaxation in dilute solution has been employed to characterize local chain motion in several polymers with aromatic backbone units. The two general types examined so far are polyphenylene oxides (1-2) and aromatic polycarbonates (3-5) and these two types are the most common high impact resistant engineering plastics. The polymer considered in this report is an aromatic polyformal (see Figure 1) where the aromatic unit is identical to that of one of the polycarbonates. This polymer has a similar dynamic mechanical spectrum to the impact resistant polycarbonates (6 ) and is therefore an interesting system for comparison of chain dynamics. 

Very large micelles may also form in binary surfactant systems. These are long wormlike micelles that become entangled at higher concentrations, giving rise to rheological properties similar to those in polymer solutions. Such systems have been examined by H band shape analysis [52,53]. The protons of the surfactant hydrocarbon chain form a very large dipolar coupled spin system with an essentially continuous distribution of transverse relaxation rates. The distribution of relaxation rates is related to the distribution of order... 

Berne and Pecora s text [16] is sometimes incorrectly cited as asserting that eq 12 is uniformly correct for light-scattering spectra. The analysis in Berne and Pecora [16] correctly obtains eq 12. However, this analysis refers the special case of a system in which particle displacements are governed by the simple Langevin equation. In these s tems, particle displacements in successive moments are uncorrelated. However, in a viscoelastic system, the polymer solution has a memory particle displacements in successive moments are no longer uncorrelated. With respect to probes in polymer solutions, Berne and Pecora s analysis is only applicable at times mtich longer than any viscoelastic relaxation times. 

In addition to the article by Jones et al. in ref. 1, several other reviews of polymer relaxation in dilute solution have appeared, filling a long-existing need. Cohen-Addadhas briefly reviewed n.m.r. in concentrated polymer solutions where entanglements lead to non-zero dipole-dipole coupling. Weill et alP have surveyed the application of n.m.r. to counterion-polyelectrolyte interactions. 

The SPH method provides an efficient way for the numerical simulations of the phase-separation phenomena in polymer blends. For instance, Okuzono used this approach to simulate a specific type of phase separation - the so-called viscoelastic phase separation - experimentally found in polymer solutions and dynamically asymmetric mixtures. Examining the effect of stress relaxation time on morphology of domains, it was shown that the more viscous phase forms network-like domains when the stress relaxation time is large. 

An interesting example of such coupling is observed in polymer solutions between the relaxation of the critical concentration fluctuations and viscoelastic relaxation. This coupling leads to a crossover between the dilfusive critical dynamics in the critical regime and relaxation dynamics of an infinite polymer chain in the theta-pomt. regime. 

Jones AA, Stockmayer WH (1977) Models for spin relaxation in dilute-solutions of randomly coiled polymers. J Polym Sci Part B Polym Phys 15(5) 847-861. doi 10.1002/pol.l977. 180150508... 

Even at very low concentrations, the viscoelastic properties are affected by in-termolecular interactions as evidenced by the extrapolation plots of Fig. 9-10. A simple analysis of the initial concentration dependence has suggested that the first effect is an increase in the longest relaxation time. Recent theoretical calculations of Muthukumar and Freed, based on the Freed-Edwards theory of concentration dependence of viscosity in polymer solutions, show that the pth.relaxation time has a concentration dependence of the form... 

---