Application to Polymer Solutions

Palit S.R., Kar I. Polynomial expansion of log relative viscosity and its application to polymer solutions. Journal of Polymer Science Part A-1, 5,10 (1967) 2629-2636. 

Gee and Orr have pointed out that the deviations from theory of the heat of dilution and of the entropy of dilution are to some extent mutually compensating. Hence the theoretical expression for the free energy affords a considerably better working approximation than either Eq. (29) for the heat of dilution or Eq. (28) for the configurational entropy of dilution. One must not overlook the fact that, in spite of its shortcomings, the theory as given here is a vast improvement over classical ideal solution theory in applications to polymer solutions. 

Panayiotou, C., Vera, J. H. (1980). The quasi-chemical approach for non-randomness in liquid mixtures. Expressions for local composition with an application to polymer solution. Fluid Phase... 

In the next section, we present a simple description of an FCS experiment especially for a biological system as an inhomogeneous medium. We also describe our recent challenge to observe anomalous diffusion by a modified FCS system and its application to polymer solutions, which is are model media for extracellular matrices. In the third section, we introduce various applications of FCS to the observation of a single cell and its surroundings. 

C. Panayiotou and J. H. Vera. 1980. The quasi-chemical approach for nonrandomness in liquid mixtures Expression for local surfaces and local compositions with an applications to polymer solutions. Fluid Phase Equilib. 5 55. 

In the cryoscopic method, the freezing temperature of a solution is compared with that of the pure solvent. The polymer must be solvable in the solvent at flie freezing temperature and must not react with the solvent either ehemieally or physically. Difficulties may arise from limited solubility and from the formation of solid solutions on freezing. Application of cryoscopy to polymer solutions is not widespread in literature despite the simplicity of the required equipment. Cryoscopy was reviewed by Glover, who also discussed technical details and problems in concern with application to polymer solutions. A detailed review on cryometers and cryoscopic measurements for low-molar mass systems was recently made by Doucet. Cryometers are sold commercially, e.g., Knauer. Measurements of thermodynamic data are infrequent. Applications usually determine molar masses. Accurate data require precise temperature measurement and control as well as caution with the initiation of the crystallization process and the subsequent establishment of equilibrium (or steady state) conditions. High purity is required for the solvent and also for the solute. 

Polymers in solutions incessantly change both their shape and position randomly by thermal agitation. This Brownian motion dominates various time-dependent phenomena in polymer solutions such as viscoelasticity, diffusion, birefringence, and dynamic light scattering, which are to be discussed in subsequent chapters. In this chapter, we study the basic theory of Brownian motion. Since the general aspects of the theory of Brownian motion have already been discussed in many articles, we shall limit the discussion to topics which will be useful in the application to polymer solutions and suspensions. 

The LB method and its improved versions are widely used for the effident treatment of polymer solution dynamics. In the application to polymer solution dynamics, the polymer itself is still treated on a partide-based CG level using, for example, a bead-spring model, while the solvent is treated on the level of a discretized Boltzmann equation. The two parts are coupled by a simple dissipative point-partide force, and the system is driven by Langevin stochastic forces added to both the fluid and the polymers. In this approach, the hydrodynamics of the low-molecular-weight solvent is correctly captured, and the HI between polymer segments, which is mediated by the hydrodynamic flow generated within the solvent through the motion of the polymer, is present in the simulation without explidt... 

The ESR working window in which the ESR line shapes are sensitive to rotational reorientation depends on the anisotropy of the A- and g-tensors of the radical for nitroxides, the range for Xp, is 10 -10 s, which means that the technique is applicable to polymer solutions, polymer gels, and solid polymers at temperatures close to or above Tg. At the X-band ESR frequency ( 9 GHz), the rotational dynamics in most liquids is usually sufficiently fast, that is, Xp,Aco 1 [where Am is a measure of the magnitude of the orientation-dependent part of the spin Hamiltonian ffj(t)] such motions (Xjj < lO s) fall within the motional narrowing (fast-motional) regime. For slower dynamics (Xp,Am > 1), more complicated slow-motional spectra are observed. ... 

Experimental aspects of light scattering and application to polymer solutions... 

The major requirements for a successful ebulliometiy experiment are thermal stability, equilibration of both concentration and temperature, temperature measurement and control and pressure measurement and control. It is an advantage of ebulliometiy to know very exactly the constant pressure applied since pressure constancy is a prerequisite of any successful experiment. Commercially sold ebulliometers have seldom been used for polymer solutions. For application to polymer solutions, the operating systems have been individually constmcted. The above-mentioned reviews explain some of these in detail which will not be repeated here as ebulliometiy is not really a practiced method to obtain solvent activities and thermodynamic data in polymer solutions. However, ebulliometiy is a basic method for the investigation of vapor-liquid equilibrium data of common binaiy liquid mixtures, and we again point to the review by Williamson,where an additional number of equilibrium stills is shown. 

Weighted residual finite element methods described in Chapter 2 provide effective solution schemes for incompressible flow problems. The main characteristics of these schemes and their application to polymer flow models are described in the present chapter. 

To illustrate the application of corresponding-states theory to polymer solution calculations, we consider two cases of sol-vent/polymer vapor-liquid equilibria. The first case we consider is that of the chloroform/polystyrene solution. The second is that of benzene/polyethylene oxide. 

For the optimal application of GPC to the separation of discrete small molecules, three factors should be considered. Solvent effects are minimal, but may contribute selectivity when solvent-solute interactions occur. The resolving power in SMGPC increases as the square root of the column efficiency (plate count). New, efficient GPC columns exist which make the separation of small molecules affordable and practical, as indicated by applications to polymer, pesticide, pharmaceutical, and food samples. Finally, the slope and range of the calibration curve are indicative of the distribution of pores available within a column. Transformation of the calibration curve data for individual columns yields pore size distributions from which useful predictions can be made regarding the characteristics of column sets. 

The application of nuclear magnetic resonance (NMR) spectroscopy to polymer systems has contributed to significant advances in understanding of their structure and dynamical properties at the molecular level. From the analytical point of view, NMR spectroscopy is particularly suitable for a determination of the polymer structure by direct observation of the protons and carbons in different structural moieties. However, until the mid-1970s the application of this technique was limited to polymer solutions and to some elastomers in the solid state with a relatively high degree of the molecular mobility which allows the observation of the motionally narrowed absorption signals. 

Dynamic light scattering has traditionally been applied to polymer solutions, and DLS results for block copolymer solutions are discussed in Chapters 3 and 4. A number of recent papers have described the application of the technique to disordered block copolymer melts (Anastasiadis et al. 1993a,6 Boudenne et al. 1996 Floudas et al. 1995 Fytas et al. 1993 Jian et al. 1994a Stepanek and Lodge 1996 Vogt et al. 1994). Due to the limited range of dynamic time-scales that can... 

Finally, for completeness in Appendix A 7.1 we consider the formal relation of the continuous chain model to a field theoretic Hamiltonian, used to describe critical phenomena in ferrornagnets. It was this relation discovered by de Genries [dG72] and extended by Des Cloizeaux [Clo75, which initiated the application of the renormalization group to polymer solutions and led to the embedding into the larger realm of critical phenomena. 

Many amorphous homopolymers and random copolymers show thermorheologically simple behavior within the usual experimental accuracy. Plazek (23,24), however, found that the steady-state viscosity and steady-state compliance of polystyrene cannot be described by the same WLF equation. The effect of temperature on entanglement couplings can also result in thermorheologically complex behavior. This has been shown on certain polymethacrylate polymers and their solutions (22, 23, 26, 31). The time-temperature superposition of thermorheologically simple materials is clearly not applicable to polymers with multiple transitions. The classical study in this area is that by Ferry and co-workers (5, 8) on polymethacrylates with relatively long side chains. In these the complex compliance is the sum of two contributions with different sets of relaxation mechanisms the compliance of the chain backbone and that of the side chains, respectively. 

Kehr M, Fatkullin N, Kimmich R (2007) Molecular diffusion on a time scale between nano-and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions Application to polymer melts. J Chem Phys 126 094903 Kirkwood JG, Riseman J (1948) The intrinsic viscosity and diffusion constant of flexible macromolecules in solution. J Chem Phys 16 565-573 Klein J (1986) Dynamics of entangled linear, branched, and cyclic polymers. Macromolecules 19(1) 105—118... 

High, M. S. Danner, R. P., "Application of the Group Contribution Lattice-Fluid EOS to Polymer Solutions," AlChE J 36, 1625 (1990). 

Viscosity of concentrated polymer Solutions. II. Application of a free-volume treatment to polymer solutions. J. Appl. Polymer Sci. 10, 21 (1966). 

Equations, which are also applicable to suspension, solution, and bulk polymerization, form an extension of the Smith-Ewart rate theory. They contain an auxiliary parameter which is determined by the rate of initiation, rate constant of termination, and volume of the porticles. The influence of each variable on the kinetics of emulsion polymerization is illustrated. Two other variables are the number of particles formed and monomer concentration in the particles. Modifications of the treatment of emulsion polymerization are required by oil solubility of the initiator, water solubility of the monomer, and insolubility of the polymer in the monomer. 

Refractive index and specific refractive index increments - (k = dn/dc) of polymers in solution have been studied extensively in connection with light scattering measurements and size exclusion chromatography applications to polymer characterization for which refractometers are used as standard concentration detectors. Contrary to the observations made in the infrared region (12), refractive index increments have been shown to be a function of the molecular weight of the polymers (2) and, in some cases, of the copolymer composition (17). Therefore, the assumptions of linearity and additivity (Eq. 1 to 4) have to be verified for each particular polymer system. In the case of styrene/acrylonitrile copolymers, there is an additional uncertainty due to the... 

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