Thermodynamics, swelling

In thermodynamics, it is common to discuss the chemical potential of a component. It is possible to determine the chemical potential of the solvent by different methods, e.g., vapour pressure measurements. In the language of thermodynamics, swelling or shrinking (de-swelhng) is a result of a difference of chemical potentials, or with other words, the driving force for the uptake of solvent (1) is a difference A/ij in chemical potentials of the solvent inside (/ i) and outside (/ii o) the polymeric phase. 

Jizhong R, Chengzhang J. 1998. The coupling effect of the thermodynamic swelling process in pervaporation. J. Membr. Sci 140 221-233. 

Key Words Crosslinked Rubber, Hory-Rehner Hypothesis, Gels, Networks, Polymer, Rubber Elasticity, Scaling Theory, Solution Thermodynamics, Swelling, Valanis-Landel Function. 

Bemdt I, Popescu C, Wortmann FJ et al (2006) Mechanics versus thermodynamics swelling in multiple-temperature-sensitive core-shell microgels. Angew Chem Int Ed 45 1081-1085... 

This thermodynamic swelling force is counterbalanced by the retractive force of the crosslinked structure. The latter is usually described by the Flory rubber elasticity theory and its variations [9]. Equilibrium is attained, in a particular solvent at a particular temperature, when the two forces become equal. Thermodynamically, this equilibrium translates to the requirement that the total change of the chemical potential, (A be equal to zero. For the case described above, that term contains chemical potential contributions from mixing, (A i)f jx, and from the elastic force, (A i)g. Thus, at equilibrium we can write ... 

Before we review ionic and solvent transfer and transport in electroactive materials, some general considerations concerning the thermodynamics, swelling and conductivity of these materials will be given. 

SAN resins show considerable resistance to solvents and are insoluble in carbon tetrachloride, ethyl alcohol, gasoline, and hydrocarbon solvents. They are swelled by solvents such as ben2ene, ether, and toluene. Polar solvents such as acetone, chloroform, dioxane, methyl ethyl ketone, and pyridine will dissolve SAN (14). The interactions of various solvents and SAN copolymers containing up to 52% acrylonitrile have been studied along with their thermodynamic parameters, ie, the second virial coefficient, free-energy parameter, expansion factor, and intrinsic viscosity (15). 

If the system is not swelled ([AGLs - AGs s] = 0 [Gp s - Gp s] = 0) and there is no labor influencing it, then Ccon = AGcom, and the temperature at which thermodynamic opportunity of reaction proceeding occurs is determined from the correlation of ph and a ... 

The parameters which characterize the thermodynamic equilibrium of the gel, viz. the swelling degree, swelling pressure, as well as other characteristics of the gel like the elastic modulus, can be substantially changed due to changes in external conditions, i.e., temperature, composition of the solution, pressure and some other factors. The changes in the state of the gel which are visually observed as volume changes can be both continuous and discontinuous [96], In principle, the latter is a transition between the phases of different concentration of the network polymer one of which corresponds to the swollen gel and the other to the collapsed one. 

The swelling pattern considered above allows us to understand the peculiarities of the behavior of SAH and the effects encountered during their application. The kinetic aspects of swelling seem to be as important as the thermodynamics of this process. Therefore, we shall touch upon some problems concerning the kinetics of hydrogel swelling and deswelling. 

Therefore, the SAH swelling and deswelling rates can be quantitatively characterized by the time t which for a given hydrogel type is determined mainly by the gel particle size. The gel instability, both mechanical and thermodynamical, constitutes an additional complication [128 -130]. 

In connection with the thermodynamic state of water in SAH, it is appropriate to consider one more question, i.e., their ability to accumulate water vapor contained in the atmosphere and in the space of soil pores. It is clear that this possibility is determined by the chemical potential balance of water in the gel and in the gaseous phase. In particular, in the case of saturated water vapor, the equilibrium swelling degree of SAH in contact with vapor should be the same as that of the gel immersed in water. However, even at a relative humidity of 99%, which corresponds to pF 4.13, SAH practically do not swell (w 3-3.5 g g1). In any case, the absorbed water will be unavailable for plants. Therefore, the only real possibility for SAH to absorb water is its preliminary condensation which can be attained through the presence of temperature gradients. 

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

Secondly, a depends on the intensity of the thermodynamic interaction as expressed by t/ i(1 —0/T), which is equal to ypi—Ki (see Chap. XII, p. 523). The larger this factor, the greater the value of a for a given M. As should have been expected, therefore, the better the solvent the greater the swelling of the molecule. Conversely, the... 

The polymer-water interaction parameter (%) of cross-linked alkyl-substituted acrylamides is a function of temperature. The degree of swelling increases as % decreases. Thermodynamic parameters for interpreting the LCST phenomenon are described elsewhere [32], Figure 10 is the plot of % versus tempera-... 

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