Swelling curve

Fig. 5. Theoretical swelling curves of gels. The reduced temperature, x, is plotted as a function of the degree of swelling, V/V . f denotes the number of counter ions per sub-polymer chain between two neighboring crosslinks...

Fig. 24a-c. a. Equilibrium radius of a NIPA gel sphere as a function of temperature. At lower temperatures the gel is swollen and at higher temperatures it is shrunken. At about 34 °C the swelling curve becomes infinitely sharp, which corresponds to the critical point, b. Relaxation time of gel volume change in response to a temperature jump, as a function of temperature, c. Thermal expansion coefficient, the relative radius change per temperature increment, also diverges at the critical point... 

In the polyelectrolyte regime, due to the presence of low-molecular salt, the osmotic pressure of ions becomes less pronounced because the concentration of salt within the network turns out to be less than the concentration of salt in the outer solution n [27]. As the concentration ns grows, the amplitude of the jump of the dependence a(x) decreases and the jump shifts to the region of better solvents (Fig. 2, curve 2). At some critical value of n, the jump on the curve a(x) disappears, i.e. collapse of the network becomes smooth (Fig. 2, curve 3). Under the subsequent increase of n, the curve a(x) becomes closer and closer to the swelling curve of corresponding neutral network (Fig. 2, curves 4). 

In order to find the influence of compression on collapse of the polymer networks, the experiments on the swelling of the deformed gels of AA-SMA in water-methanol and water-dioxane mixtures were performed [29]. It was shown that uniaxial compression of the gel really affects the swelling curves and that, in a good agreement with the theory, the region of stability of the collapsed state increases and the sharpness of collapse decreases under compression. 

Fig. 1. Equilibrium swelling curves of NIPA gel in a DMSO/water mixture plotted as a function of temperature. The concentrations of DMSO are O 0% 3% A 5% A7%...

Fig. 4. Equilibrium swelling curves of NIPA (A), NNPA (O) and NCPA ( ) gels...

The volume phase transition is sensitive to many types of additives. Figure 6 shows swelling curves of the NIPA gel in aqueous solutions of SDS at various... 

Fig. 7. Equilibrium swelling curves of NIPA gel in aqueous solutions in the presence of inorganic salts. Hie concentration of salts is 1 x 10 1 [molL-1]. water (no additive) Nat KI A NaBr, KBr, O NaCl KC1...

Fig. 15. Equilibrium swelling curves calculated with Eq. (15) for various values of/ neglecting the hydrophobic interaction term. Tt = 273.15 K m = 100 P = l...

Fitting the swelling curves of Fig. 7a to the form Q(t) — kt yields values of a greater than or equal to 0.8. Thus the swelling must be considered anomalous, or non-Fickian. In the absence of ionic interactions, this would not be expected since BMA/DMA 70/30 is initially not far below its Tg at 25 °C. Indeed, swelling measurements of this copolymer in hexane show kinetics that are nearly Fickian (a 0.55), as shown in Fig. 7b. Therefore, the anomalous swelling observed in Fig. 7a must be attributed to ion transport and binding rates in the gel. We will return to this point later. 

The experiments were repeated but were not reproducible Acrylamide gels were made anew with various recipes and their swelling curves were determined as a function of acetone concentration, but they were all continuous. It took a couple of months to recognize that the gels that showed the discontinuous transition were old ones, that is, gels prepared a month earlier and left within the tubes in which they were polymerized. Subsequent experiments were all carried out on new gels, and, therefore, underwent a continuous transition. At that time all the old gels were used up, and none were left in the laboratory. 

Swelling curves of two neutral NIPA gels with different initial polymer concentration crosslinking density Nc/V0 are shown in Fig. 3 [20], One sample (call it gel A) had 0 = 0.075 and Nc/V0 = 1.02 x 1022, which undergoes a slightly discontinuous transition as shown in Fig. 3a, while the other (gel B) had <))0 = 0.114 and Nc/V0 = 2.40 x 1022, which undergoes a continuous transition as shown in Fig. 3b. In the former sample, the coexistence of the swollen and the shrunken phases was observed within 0.05 °C of the transition temperature, which is concrete evidence that the transition is discontinuous. On the other hand, the latter sample was homogeneous, at least by visual inspection,... 

The value of %2 was deduced from the jump at the transition of and that of calculated %, because these two quantities should be proportional with each other. The value thus obtained was %2 = 0.6 + 0.1. In the actual calculation, the values of Ah, As, and x2 were adjusted within the error limits so that the calculated swelling curve fits the measured one as closely as possible. The results of calculation [21] are shown in Fig. 5a and b, where they should be compared with Fig. 3a and b, respectively. The parameter values used are given in Table 2. Of course the values of Ah, As, and %2 include relatively large arbitrariness, although the fact that we can fit the observed swelling curves using reasonable values of the parameters shows that this theory captures an essential point of the phase transition of neutral gels. 

Swelling curves of NIPA-sodium acrylate (SA) copolymer gels have been measured [7] by the same method as applied to neutral gels using cylindrical samples. The concentration of NIPA (700-572 mM) and SA (0-128 mM) were... 

One very important phenomenon observed during the measurement of the discontinuous swelling curves should be mentioned here. It is the coexistence of different phases in a single sample around the transition. It has already been... 

Below, I will first describe the observation on thin cylinders because the phase coexistence can most clearly be observed in these samples and, moreover, samples of this shape are most frequently used in various experiments. The results of the observation are depicted schematically in Fig. 12. As the temperature was increased from the swollen phase, the sample gradually shrunk following the swelling curve (Fig. 7) and the onset of the transition region was manifested by the appearance of a nucleus of the high-temperature (shrunken) phase at the end of the cylinder. We denote this temperature as Tt. As long as... 

In this way, the first-order transition in plates, cubes, and thick rods proceeds in a manner quite different from that in thin rods. Because of the irregular deformation of the sample, it is clearly impossible to measure the swelling curve on these samples with the first method (measuring the characteristic length of the sample with a microscope) as explained in Sect. 3. Even though no clear phase boundary is formed, the coexistence of the swollen and shrunken phases is also realized in these samples. 

The continuous swelling curve such as depicted in Fig. 14b will be obtained even with the first method if we measure not only the diameters at one particular... 

The swelling behavior of poly(N-isopropylacrylamide) has been studied extensively [18,19]. It has been shown that this gel has a lower critical point due to the hydrophobic interaction. Such a swelling curve is schematically illustrated in Fig. 9. The gel is swollen at a lower temperature and collapses at a higher temperature if the sample gel is allowed to swell freely in water. The volume of the gel changes discontinuously at 33.6°C. The swelling curves obtained in this way correspond to the isobar at zero osmotic pressure. On the other hand, the friction coefficient is measured along the isochore, which is given in Fig. 9,... 

Fig. 9. The swelling curve of the poly(/V-isop-ropylacrylamide) gel is schematically shown. The isobar curve (thick line) corresponds to the zero osmotic pressure. The dotted line indicates the experimental path at which the volume is fixed at the initial volume V0 (the volume at which the gel is prepared)...

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