Concentration dependence, polymer-solvent

The separation of Hquid crystals as the concentration of ceUulose increases above a critical value (30%) is mosdy because of the higher combinatorial entropy of mixing of the conformationaHy extended ceUulosic chains in the ordered phase. The critical concentration depends on solvent and temperature, and has been estimated from the polymer chain conformation using lattice and virial theories of nematic ordering (102—107). The side-chain substituents govern solubiHty, and if sufficiently bulky and flexible can yield a thermotropic mesophase in an accessible temperature range. AcetoxypropylceUulose [96420-45-8], prepared by acetylating HPC, was the first reported thermotropic ceUulosic (108), and numerous other heavily substituted esters and ethers of hydroxyalkyl ceUuloses also form equUibrium chiral nematic phases, even at ambient temperatures. 

In this sense, the underlying reason of the dependence on alkali concentration 1s similar to, yet different from, the concentration dependence of solvent diffusion in polymers. 

Polymer solution viscosity is dependent on the concentration of the solvent, the molecular weight of the polymer, the polymer composition, the solvent composition, and the temperature. More extensive information on the properties of polymer solutions may be found ia refereaces 9 and 54—56. 

Gelatin stmctures have been studied with the aid of an electron microscope (23). The stmcture of the gel is a combination of fine and coarse interchain networks the ratio depends on the temperature during the polymer-polymer and polymer-solvent interaction lea ding to bond formation. The rigidity of the gel is approximately proportional to the square of the gelatin concentration. Crystallites, indicated by x-ray diffraction pattern, are beUeved to be at the junctions of the polypeptide chains (24). 

The role of specific interactions in the plasticization of PVC has been proposed from work on specific interactions of esters in solvents (eg, hydrogenated chlorocarbons) (13), work on blends of polyesters with PVC (14—19), and work on plasticized PVC itself (20—23). Modes of iateraction between the carbonyl functionaHty of the plasticizer ester or polyester were proposed, mostly on the basis of results from Fourier transform infrared spectroscopy (ftir). Shifts in the absorption frequency of the carbonyl group of the plasticizer ester to lower wave number, indicative of a reduction in polarity (ie, some iateraction between this functionaHty and the polymer) have been reported (20—22). Work performed with dibutyl phthalate (22) suggests an optimum concentration at which such iateractions are maximized. Spectral shifts are in the range 3—8 cm . Similar shifts have also been reported in blends of PVC with polyesters (14—20), again showing a concentration dependence of the shift to lower wave number of the ester carbonyl absorption frequency. 

Experimental values of X have been tabulated for a number of polymer-solvent systems (4,12). Unfortunately, they often turn out to be concentration and molecular weight dependent, reducing their practical utility. The Flory-Huggins theory quahtatively predicts several phenomena observed in solutions of polymers, including molecular weight effects, but it rarely provides a good quantitative fit of data. Considerable work has been done subsequentiy to modify and improve the theory (15,16). 

Vrentas, JS Duda, JL, Diffusion in Polymer-Solvent Systems. I. Reexamination of the Free-Volume Theory, Journal of Polymer Science Polymer Physics Edition 15, 403, 1977. Vrentas, JS Duda, JL, Diffusion in Polymer-Solvent Systems. II. A Predictive Theory for the Dependence of Diffusion Coefficients on Temperature, Concentration, and Molecnlar Weight, Journal of Polymer Science Polymer Physics Edition 15, 417, 1977. 

In this chapter, the subscript 1 denotes the penetrant and subscript 2, the polymer. The term penetrant refers to solvents which have sufficient thermodynamic affinity for and interaction with the polymer. It is because of this interaction that penetrant diffusion exhibits a significant concentration dependence. This orientation excludes consideration of the permeation of small gaseous molecules. 

When applied to a volume-fixed frame of reference (i.e., laboratory coordinates) with ordinary concentration units (e.g., g/cm3), these equations are applicable only to nonswelling systems. The diffusion coefficient obtained for the swelling system is the polymer-solvent mutual diffusion coefficient in a volume-fixed reference frame, Dv. Also, the single diffusion coefficient extracted from this analysis will be some average of concentration-dependent values if the diffusion coefficient is not constant. 

Fig. 58a, b. Segmental diffusion in semi-dilute polymer solutions. Schematic view of the Q-dependence of the relaxation rates Q(Q) at a fixed concentration. a Good solvent conditions b -conditions. (Reprinted with permission from [168]. Copyright 1994... 

Flory proposed a semiempirical expression to predict the concentration dependence of the melting curve of long-chain polymers mixed with small solvent molecules [75] ... 

The dependence of the fluorescence quantum yields and lifetimes of these stabilizers on the nature of the solvent suggests that the excited-state, non-radiative processes are affected by solvation. In polar, hydroxylic solvents, values of the fluorescence quantum yield for the non proton-transferred form are significantly lower, and the fluorescence lifetimes are shorter, than those calculated for aprotic solvents. This supports the proposal of the formation, in alcoholic solvents, of an excited-state encounter complex which facilitates ESIPT. The observed concentration dependence of the fluorescence lifetime and intensity of the blue emission from TIN in polymer films provides evidence for a non-radiative, self-quenching process, possibly due to aggregation of the stabilizer molecules. 

V, is the molar volume of polymer or solvent, as appropriate, and the concentration is in mass per unit volume. It can be seen from Equation (2.42) that the interaction term changes with the square of the polymer concentration but more importantly for our discussion is the implications of the value of x- When x = 0.5 we are left with the van t Hoff expression which describes the osmotic pressure of an ideal polymer solution. A sol vent/temperature condition that yields this result is known as the 0-condition. For example, the 0-temperature for poly(styrene) in cyclohexane is 311.5 K. At this temperature, the poly(styrene) molecule is at its closest to a random coil configuration because its conformation is unperturbed by specific solvent effects. If x is greater than 0.5 we have a poor solvent for our polymer and the coil will collapse. At x values less than 0.5 we have the polymer in a good solvent and the conformation will be expanded in order to pack as many solvent molecules around each chain segment as possible. A 0-condition is often used when determining the molecular weight of a polymer by measurement of the concentration dependence of viscosity, for example, but solution polymers are invariably used in better than 0-conditions. 

When the temperature is increased above the 0-temperature the enhanced local viscosity at higher concentration drops. The variation is the same as observed for the macroscopic viscosity [329]. In [328] polyisoprene (PI) and PS in different solvents have also been investigated and the authors observe that the slopes of the concentration dependence of the scaled local viscosities for PS and PI have a ratio of 1.7, which matches the value of the concentration ratio either on the Kuhn length (1.6) or the persistence length (1.7) for the two polymers. 

The concentration dependence of polymer or solvent motion has been studied only rarely over a wide range in concentration. Typically, polymer carbon-13 relaxation is not concentration dependent up to 20-30 percent polymer. Little is known concerning the concentration dependence of the solvent motion. 

Figure 9. Temperature and concentration dependence of the solvent proton-polymer proton relaxation rate (0), 10% polymer (X), 20% polymer.

A theoretical expression for the concentration dependence of the polymer diffusion coefficient is derived. The final result is shown to describe experimental results for polystyrene at theta conditions within experimental errors without adjustable parameters. The basic theoretical expression is applied to theta solvents and good solvents and to polymer gels and polyelectrolytes. 

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