Free swelling coefficient

Olivier (1979) proposed the geodurability classification, which is based on the free-swelling coefficient and uniaxial compressive strength (Fig. 3.5). This classification was developed to assess the durability of mudrocks. 

Both factors contribute to the free energy of a swollen polymer coil (with swelling coefficient a), F a) = U a) TS a) (see Section 7.8, Equation 7.19). The potential energy term U a) is determined by the repulsive interactions (see (8.8)) ... 

The function F a) is sketched in Figure 8.4. You can see a minimum in the curve at a certain a. The minimum of the free energy always gives the equilibrium state. So the equilibrium swelling coefficient is just the value of a at the minimum. Notice that the unknown numerical value of the coefficient 7 does not affect the qualitative shape of F a) curve, but does somewhat affect the value of a in the minimum. 

One of the simplest ways to determine the gel diffusion coefficient (D) is by means of free swelling experiment [5-7]. Since our actuator is driven by means of temperature changes, the free swelling kinetic is coupled to the heat transmission one due to thermal diffusion and interstitial fluid convection. 

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). 

Further development of the Flory-Huggins method in direction of taking into account the effects of far interaction, swelling of polymeric ball in good solvents [4, 5], difference of free volumes of polymer and solvent [6, 7] leaded to complication of expression for virial coefficient A and to growth of number of parameters needed for its numerical estimation, but weakly reflected on the possibility of equation (1) to describe the osmotic pressure of polymeric solutions in a wide range of concentrations. 

Both the Yasuda et al. and Schnitzer theories indicate that the key variables defining permeability in a gel are the swelling degree of the gel and the average dimension of the solute. Thus the dependence of permeability on swelling degree for a responsive gel inert to solutes can be predicted using the theory of Yasuda et al. to obtain the ratio D/Dc (the ratio of the diffusion coefficient of a solute in the gel to its value in free solution) and the theory of Schnitzer for ideal size exclusion to obtain K. A dimensionless permeability can be defined as the... 

Fig. 16. The diffusion coefficient of acetaminophen in 10 x 4 PNIPAAm gels falls as the swelling degree (Q) of the gel decreases due to increasing temperature. Below the transition temperature of the gel, the linear relationship between log D and (Q — 1) 1 predicted by the free volume theory of Yasuda et al. [10] is observed. Above the transition temperature, the theory underestimates D by 35 times. Reprinted from the Journal of Controlled Release (1992) 18 1, by permission of the publishers, Elsevier Science Publishers BV [70]...

Fig. 17. Vitamin B12 diffusion coefficients vs polyfacrylamide-co-sodium methacrylate) gel swelling. The variation is that expected from free volume theories. Reprinted with permission from Chemical Engineering Science, 44,...

The orientation of the swelling agent (solvent or free chains) has to be taken into account in the analysis of the stress-optical behaviour of swollen networks. Specifically, the segment polarisability (relative to the network chains or to the diluent chains), as currently derived from stress-optical coefficients [33], may not be representative of intrinsic properties of isolated chains. Short-range orientational interactions between the probe molecules and network chains (and between the chains of the matrix itself) must be considered in the interpretation of opticoelastic properties of swollen (and dry) rubbers [67]. 

Since the separate time scale condition is clearly valid for most of the polymerization process, one may say that each polymer chain is formed inside a particle of unchanging siz wherein all rate coefficients are constant and the distribution of free radicals has its steady-state value, for each volume V. Any residual effect of the PSD on the MWD would reside presumably in the effects of the PSD on the kinetic parameters (e.g., p. c, and to a lesser extent fc). Conversely, the MWD would possibly influence the PSD through its effects on the swelling of the particles by the monomer the effect, if it exists, is likely to ha small. 

The diffusivity is not only a function of temperature and pressure, but also concentration of dissolved CO2. The diffusivity increases as the temperature increases and decreases as the pressure increases. When CO2 dissolves, the polymer swells and its free volume increases. The diffusion coefficient then becomes larger... 

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