Swelling, degree

These parameters are related to one another and can be determined theoretically or through the use of a variety of experimental techniques. Usually they are calculated from typical macroscopic network properties, like swelling degree Q or Young s modulus E (for tensile or compression strain) or shear modulus G (for shearing strain), which can be determined by physical methods as will be shown in Sections 4.S.2-4.3.4. 

Simple models assume ideal networks. However, real polymer networks contain network defects, like free chain ends (dangling ends), rings, and entanglements (Fig. 4.14), which sensitively affect mechanical properties and also swelling behavior. 

One of the most important properties of hydrogel networks is their swelling degree. Due to water absorption into the network, the macroscopic dimensions of the cross-hnked bulk polymer increase until an equilibrium is reached at which the decrease in free energy due to mixing of the polymer chains with 

The volume degree of swelling of cross-hnked polymers is simply the inverse of the polymer volume fraction. For a cylindrical sample, can be obtained from the diameter of the swollen d and the dry cylinder as 

Alternatively, the equilibrium swelling degree can be defined as the ratio of the swollen polymer mass to the mass of the dry polymer  

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Table 3 Influence of Radiation Dose on the Copolymer Composition and the Swelling Degree...

The influence of radiation dose on the polymer composition and the swelling degree of (pAM-DAEA-HCl) are shown in Table 3. The results show that the percent of acrylamide in the copolymer is higher than that of the amine. This can be attributed to smaller reactivity ratios of monomers of diallylammonium salts relative to acryl-... 

Judging from the extraction percentage of PVAc and from the swelling degree of latex films in acetone, it is... 

Aldehydes (glutaric, succinic [53-56]) are used to crosslink PVA, the network density being controlled by the ratio of aldehyde to OH-groups. The swelling degree of these hydrogels does not exceed 35-40 ml g-1, and there are almost quantitative correlations of the network density with the crosslinker concentration... 

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 traditional methods for measuring the swelling degree [100] are, as a rule, limited due to the difficulties in quantitative separation of the swollen gel from the outer solution because of extremely low strength of the former. These difficulties can be avoided by measuring the dimensions of a regular shape sample directly in an excess of liquid [19, 101,102], The other example is the modified volumetric method recently developed by us especially for SAH [103],... 

Of particular importance for the application are the effects of the external compression and the ionic composition of the outer solution on the swelling degree. The reason is that hydrogels usually exist in mineralized aqueous solutions (soil solution) and are affected by compression, for example, produced by the surrounding particles of the soil. Even in the absence of any external load the compression develops due to the gel swelling in a constrained volume. 

When the ionic composition varies within the range of very low salt concentrations, the swelling degree can reach its maximum [101]. This behavior is observed... 

Fig. 2. Dependencies of the swelling degree of PAAm hydrogels on the concentration X (in mol L-1) of H+ (/), Ca2+ (2), and Na+ (3) in the solution. Dashed curve 3 is obtained by calculation. From Dubrovskii et al. [22]...

In contrast to polyelectrolyte hydrogels, nonionic ones are almost insensitive to the ionic composition of the medium. In particular, the equilibrium swelling degree of a charge-free PAAm gel practically does not depend on the Cu2 + concentration (Fig. 4, curve 0) nor on the concentration of several other ions or on the pH value [101]. 

Osmotic deswelling experiments, performed with a series of PAAm [20] and PVA [112] gels have revealed a correlation between their sensitivity to the external pressure and the equilibrium swelling degree in the absence of external forces. This fact is illustrated below ... 

An increase in the swelling degree usually results in lowering elastic modulus. According to the rubber elasticity theory [116-118] the shear modulus of the gel G can be expressed as ... 

Various modifications of the Flory theory [4] are usually applied to describe the uncharged gels. Their crosslinking density can be simply calculated from the swelling degree using Eqs. (3.1) and (3.2) or analytical expressions for the Mc value (see, for example, Ref. [124]). 

These equations allow either to predict the swelling degree (w = l/(p) as a function of external conditions or to calculate the network parameters from the correlation between the theoretical and experimental dependencies w(q) or w(p) [22, 102], An example of such a correlation is given in Fig. 2 and 5. As can be seen, theoretical predictions are in good agreement with experimental data. However, when the outer solution contains multivalent cations, only a semi-quantitative agreement is attained. 

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. 

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