Polymer Solution Parameters

Heinzelmann [49] and Briston [52] have given details of these methods. The main problem with direct coating is that incompatibility of the porous support with polymer solution can result in the formation of pinholes in the membranes. However, this problem can be overcome if care is taken to ensure sufficient wetting of the support by the polymer solution. Parameters that can be varied in optimizing the process for a defect free membrane are... 

Let us note in conclusion, that all widespreading in traditional physics-chemistry of polymer solutions parameters are cormected in any case with macromo-lecular coil stracture, characterizing its fractal dimension D. This circumstance for itself speaks about a very important role of the indicated factor [28],... 

Polymer solution parameters are certain variables related to the physical properties of the polymer solution used for electrospinning nanofibers such as polymer concentration, polymer solution viscosity, polymer molecular weight, solution charge density, conductivity, volatility, surface tension, dielectric constant, and dipole moment. These variables are hard to be altered since changing one of those variables would consequently change some of the others. An example of that is the alteration in the polymer solution viscosity upon changing its conductivity (Pham et al. 2006). 

The experimental data can be treated on the basis of statistical theories of polymer solutions. Parameter%i2 (pol3rmer-solvent) may be presented in the... 

In polymer solutions and blends, it becomes of interest to understand how the surface tension depends on the molecular weight (or number of repeat units, IV) of the macromolecule and on the polymer-solvent interactions through the interaction parameter, x- In terms of a Hory lattice model, x is given by the polymer and solvent interactions through... 

Figure A2.5.27. The effective coexistence curve exponent P jj = d In v/d In i for a simple mixture N= 1) as a fimction of the temperature parameter i = t / (1 - t) calculated from crossover theory and compared with the corresponding curve from mean-field theory (i.e. from figure A2.5.15). Reproduced from [30], Povodyrev A A, Anisimov M A and Sengers J V 1999 Crossover Flory model for phase separation in polymer solutions Physica A 264 358, figure 3, by pennission of Elsevier Science.

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

At first glance, the contents of Chap. 9 read like a catchall for unrelated topics. In it we examine the intrinsic viscosity of polymer solutions, the diffusion coefficient, the sedimentation coefficient, sedimentation equilibrium, and gel permeation chromatography. While all of these techniques can be related in one way or another to the molecular weight of the polymer, the more fundamental unifying principle which connects these topics is their common dependence on the spatial extension of the molecules. The radius of gyration is the parameter of interest in this context, and the intrinsic viscosity in particular can be interpreted to give a value for this important quantity. The experimental techniques discussed in Chap. 9 have been used extensively in the study of biopolymers. 

Dilute Polymer Solutions. The measurement of dilute solution viscosities of polymers is widely used for polymer characterization. Very low concentrations reduce intermolecular interactions and allow measurement of polymer—solvent interactions. These measurements ate usually made in capillary viscometers, some of which have provisions for direct dilution of the polymer solution. The key viscosity parameter for polymer characterization is the limiting viscosity number or intrinsic viscosity, [Tj]. It is calculated by extrapolation of the viscosity number (reduced viscosity) or the logarithmic viscosity number (inherent viscosity) to zero concentration. 

The crowning development in MW determination was the invention of gel permeation chromatography, the antecedents of which began in 1952 and which was finally perfected by Moore (1964). A column is filled with pieces of cross-linked macroporous resin and a polymer solution (gel) is made to flow through the column. The polymer solute permeates the column more slowly when the molecules are small, and the distribution of molecules after a time is linked not only to the average MW but also, for the first time with these techniques, to the vital parameter of MW distribution. 

The reversible aggregation of monomers into linear polymers exhibits critical phenomena which can be described by the 0 hmit of the -vector model of magnetism [13,14]. Unlike mean field models, the -vector model allows for fluctuations of the order parameter, the dimension n of which depends on the nature of the polymer system. (For linear chains 0, whereas for ring polymers = 1.) In order to study equilibrium polymers in solutions, one should model the system using the dilute 0 magnet model [14] however, a theoretical solution presently exists only within the mean field approximation (MFA), where it corresponds to the Flory theory of polymer solutions [16]. 

The peak width increases with injection volume. Therefore this parameter has to be fixed for comparative measurements. It has become the custom to inject low molecular weight test samples in very small volumes at very high concentrations, occasionally even as pure compounds. This extreme is not recommended as it is more important to inject a constant sample amount, reproducibly, in a precisely kept volume. Typical GPC injections are between 50 and 200 /a1. It is better to inject a larger volume of a lower concentration polymer solution. GPC units are often not designed for injection volumes lower... 

Fig. 31. Bubble wall velocity vs time during cavitational collapse for different values of the parameter X defined as X ss 0.4 c iTl] p./fri/2 (Ph — Pv)i/2). X permits us to account for the viscous and inertia effects of the polymer solution (redrawn according to Ref. [122]) ...

From the outset, Flory (6) and Huggins (4,5 ) recognized that their expressions for polymer solution thermodynamics had certain shortcomings (2). Among these were the fact that the Flory-Huggins expressions do not predict the existence of the LCST (see Figure 2) and that in practice the x parameter must be composition dependent in order to fit phase equilibrium data for many polymer solutions 3,8). 

To recapitulate, the Flory version of the Prigogine free-volume or corresponding-states polymer solution theory requires three pure-component parameters (p, v, T ) for each component of the solution and one binary parameter (p ) for each pair of components. 

The polymer solubility can be estimated using solubility parameters (11) and the value of the critical oligomer molecular weight can be estimated from the Flory-Huggins theory of polymer solutions (12), but the optimum diluent is still usually chosen empirically. 

Xylan-based micro- and nanoparticles have been produced by simple coacervation (Garcia et al., 2001). In the study, sodium hydroxide and chloride acid or acetic acid were used as solvent and non-solvent, respectively. Also, xylan and surfactant concentrations and the molar ratio between sodium hydroxide and chloride acid were observed as parameters for the formation of micro- and nanoparticles by the simple coacervation technique (Garcia et al., 2001). Different xylan concentrations allowed the formation of micro- and nanoparticles. More precisely, microparticles were found for higher concentrations of xylan while nanopartides were produced for lower concentrations of the polymer solution. When the molar ratio between sodium hydroxide and chloride acid was greater than 1 1, the partides settled more rapidly at pH=7.0. Regarding the surfactant variations, an optimal concentration was found however, at higher ones a supernatant layer was observed after 30 days (Garda et al., 2001). 

Theta temperature is one of the most important thermodynamic parameters of polymer solutions. At theta temperature, the long-range interactions vanish, segmental interactions become more effective and the polymer chains assume their unperturbed dimensions. It can be determined by light scattering and osmotic pressure measurements. These techniques are based on the fact that the second virial coefficient, A2, becomes zero at the theta conditions. 

This stipulation of the interaction parameter to be equal to 0.5 at the theta temperature is found to hold with values of Xh and Xs equal to 0.5 - x < 2.7 x lO-s, and this value tends to decrease with increasing temperature. The values of = 308.6 K were found from the temperature dependence of the interaction parameter for gelatin B. Naturally, determination of the correct theta temperature of a chosen polymer/solvent system has a great physic-chemical importance for polymer solutions thermodynamically. It is quite well known that the second viiial coefficient can also be evaluated from osmometry and light scattering measurements which consequently exhibits temperature dependence, finally yielding the theta temperature for the system under study. However, the evaluation of second virial... 

The thermodynamic behavior of the dilute polymer solution depends on three factors (1) the molecular weight, (2) the thermodynamic interaction parameters and ki, or ipi and 0, which characterize the segment-solvent interaction, and (3) the configuration, or size, of the... 

Parameter occurring in thermodynamic relations for dilute polymer solutions (Chaps. XII and XIV). 

Since [n] is a physically measurable quantity and is more directly relatable than the usual SEC calculated Mn and Mw values to the macroscopic viscosity parameters of the polymer solution, a routine SEC-[n] method brings SEC a step closer to practical evaluation of the strength and processibility of different polymer samples. 

Several assumptions were made in using the broad MWD standard approach for calibration. With some justification a two parameter equation was used for calibration however the method did not correct or necessarily account for peak speading and viscosity effects. Also, a uniform chain structure was assumed whereas in reality the polymer may be a mixture of branched and linear chains. To accurately evaluate the MWD the polymer chain structure should be defined and hydrolysis effects must be totally eliminated. Work is currently underway in our laboratory to fractionate a low conversion polydlchlorophosphazene to obtain linear polymer standards. The standards will be used in polymer solution and structure studies and for SEC calibration. Finally, the universal calibration theory will be tested and then applied to estimate the extent of branching in other polydlchlorophosphazenes. 

To reduce or eliminate polymer solute/glass packing interactions the following parameters were optimized a) pH, ionic strength and concentrations of additives such as nonionic surfactants, b) selection of pore sizes in a column combination. 

Below a critical concentration, c, in a thermodynamically good solvent, r 0 can be standardised against the overlap parameter c [r)]. However, for c>c, and in the case of a 0-solvent for parameter c-[r ]>0.7, r 0 is a function of the Bueche parameter, cMw The critical concentration c is found to be Mw and solvent independent, as predicted by Graessley. In the case of semi-dilute polymer solutions the relaxation time and slope in the linear region of the flow are found to be strongly influenced by the nature of polymer-solvent interactions. Taking this into account, it is possible to predict the shear viscosity and the critical shear rate at which shear-induced degradation occurs as a function of Mw c and the solvent power. 

K. K. K. Chao, M. C. Williams 1983, (The ductless siphon A useful test for evaluating dilute polymer solution elonga-tional behavior. Consistency with molecular theory and parameters), J. Rheol. 27 (5), 451 174. 

An alternative to the rotating disk method in a quiescent fluid is a stationary disk placed in a rotating fluid. This method, like the rotating disk, is based on fluid mechanics principles and has been studied using benzoic acid dissolving into water [30], Khoury et al. [31] applied the stationary disk method to the study of the mass transport of steroids into dilute polymer solutions. Since this method assumes that the rotating fluid near the disk obeys solid body rotation, the stirring device and the distance of the stirrer from the disk become important considerations when it is used. A similar device was developed by Braun and Parrott [32], who used stationary spherical tablets in a stirred liquid to study the effect of various parameters on the mass transport of benzoic acid. 

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