Solvent volume fraction and

The high temperature endothermic peak can be treated thermodynamically, because its temperature and intensity are dependent on the solvent volume fraction and independent of the heating rate, as observed by Donovan. This behaviour has been treated quantitatively, using Flory s relationship between the melting point of the crystalline phases and the quantity of added water [15,45]. This relation between melting point and water content is shown in Equation 4.1 and its equivalent. Equation 4.2 ... 

Charged particles in polar solvents have soft-repulsive interactions (see section C2.6.4). Just as hard spheres, such particles also undergo an ordering transition. Important differences, however, are that tire transition takes place at (much) lower particle volume fractions, and at low ionic strengtli (low k) tire solid phase may be body centred cubic (bee), ratlier tlian tire more compact fee stmcture (see [69, 73, 84]). For tire interactions, a Yukawa potential (equation (C2.6.11)1 is often used. The phase diagram for the Yukawa potential was calculated using computer simulations by Robbins et al [851. 

In this equation < > and -q, are the volume fraction and viscosity of the pure polymer at the temperature under consideration. The subscript 2 refers to the solvent or plasticizer. 

The adsorption of block and random copolymers of styrene and methyl methacrylate on to silica from their solutions in carbon tetrachloride/n-heptane, and the resulting dispersion stability, has been investigated. Theta-conditions for the homopolymers and analogous critical non-solvent volume fractions for random copolymers were determined by cloud-point titration. The adsorption of block copolymers varied steadily with the non-solvent content, whilst that of the random copolymers became progressively more dependent on solvent quality only as theta-conditions and phase separation were approached. 

Figure 14. Solvent (water, methanol) diffusion coefficients of (a) Nafion 117 (EW =1100 g/equiv) and (b) sulfonated poly(arylene ether ketone)s, as a function of the solvent volume fraction. Self-diffusion data (AiaO. T eOi-i) are taken from refs 197, 224, 226, 255—263 and unpublished data from the laboratory of one of the authors) chemical diffusion coefficients (Z>h2o) are calculated from self-diffu-sion coefficients (see text), and permeation diffusion coefficients are determined from permeation coefficients. ...

F eOH FH20, and Fmgoh) for different solvated acidic polymers are presented in a way that allows some interesting comparisons and the calculation or estimation of the elements of the transport matrix Ljj. In many publications, these transport parameters are reported as a function of the solvent content and are expressed as the number of solvent molecules (i.e., water) per sulfonic acid group. Because of the importance of percolation effects in all considered transport coefficients, we have converted these solvent contents to solvent volume fractions, except for proton conductivities, as shown in Figures 17 and 18. 

The transport properties that are most significantly affected by changes of the water volume fraction are the water/methanol electro-osmotic drag and permeation, both of which have significant contributions from viscous flow (see Section 3.2.1.1). For DMFC applications (where the membrane is in contact with a liquid water/methanol mixture), this type of transport determines the crossover, which is only acceptably low for solvent volume fractions smaller than 20 vol % (see Figures 14 and 15). Consequently, recent attempts have been focused on strengthening... 

A is the initial concentration 9 of the strong solvent in the mobile phase at the start of the gradient (usually expressed in terms of volume fractions) and B or B are the steepness (slope) of the gradient, i.e., the increase in 9 in the time unit, or in the volume unit of the mobile phase,... 

Taking into account the modes in which the water can be sorbed in the resin, different models should be considered to describe the overall process. First, the ordinary dissolution of a substance in the polymer may be described by the Flory-Huggins theory which treats the random mixing of an unoriented polymer and a solvent by using the liquid lattice approach. If as is the penetrant external activity, vp the polymer volume fraction and the solvent-polymer interaction parameter, the relationship relating these variables in the case of polymer of infinite molecular weight is as follows ... 

The effect of solvent may be separated into heat and entropy terms, the former given by the difference in the molar heats of dilution of the monomer and polymer solutions from the standard solvent volume fractions to their equilibrium fractions s. The entropy term is constant... 

Values of a can be determined to 0.01, varying between 0 and 3.5, and reflect the affinity of the functional group of the solvent to the phenyl ring on the one hand and the steric hindrance due to the molecular bulk of the solvent on the other. It was also shown (Errede 1989) that the Flory-Huggins interaction parameter % at solvent volume fractions cp in the solvent-copolymer system is given by ... 

The self-diffusion of benzene in PIB [36], cyclohexane in BR [37] and toluene in PIB [38-40] has been investigated by PFG NMR. In addition more recently Schlick and co-workers [41] have measured the self-diffusion of benzene and cyclohexane mixtures in polyisoprene. In the first reported study of this kind, Boss and co-workers [36] measured the self-diffusion coefficients of benzene in polyisoprene at 70.4 °C. The increase in Dself with increasing solvent volume fraction could be described by the Fujita-Doolittle theory which states that the rate of self-diffusion scales with the free volume which in turn increases linearly with temperature. At higher solvent volume fractions the rate of selfdiffusion deviates from the Fujita-Doolittle theory, as the entanglement density decreased below the critical value. 

Figure 13.2 Self-diffusion coefficients of cyclohexane in BR solutions as a function of temperature and solvent volume fraction (Vj = 0.05 (O), 0.19 ( ), 0.29 ( ), 0.375 ( ) and 0.45 (A) [37]. The solid and dashed lines are best fits to the WLF equation [37]...

Figure 5.2. Free-energy change of mixing for rods and solvent molecules. Free energy change (AGIRT) of (A) solid phase associated with transfer of a solute molecule (macromolecule) from the liquid to the solid state as a function of solute volume fraction (V2) for low (Z = 10) and high (Z = 200) axial ratios and (B) liquid phase as a function of solute volume fraction in the presence (Xi = 0.1) and absence (Xi = 0) of interactions between solute molecules. The diagrams show that separation of solute and solvent molecules occurs spontaneously for high axial ratios above a critical volume fraction and that the free energy of the solvent is raised by inter-molecular interactions.

FIGURE 17 Representative plots of In lc[ versus the volume fraction organic solvent for two polypeptides (namely the all L-a-polypeptide, I, NH2- DDALYDDKNWDRAPQRCYYQ-COOH (A) and its all D-a-retro-inverso isomer, 2, NH2-QYYCRQPARDWNKDDYLADD-COOH (B) determined by RP- HPLC methods over the organic solvent volume fraction range of i//= 0.17 to i// = 0.21 with water-acetonitrile mixtures and from ifi = 0.35 to with water - methanol mixtures (C) and (D), respectively, and from temperatures of 278 to 338 K in 5 K increments. Data adapted from Ref. 62. 

Figure 1. Cluster integral, G lv, versus solvent volume fraction (the solid line was calculated by us) (A) the toluene (1) + polystyrene (2) system (, ref 1), (B) the water (1) + collagen (2) system (, ref 12), (C) the water (1) + serum albumin (2) system, (D) the water (1) + hydroxypropyl cellulose (2) system, and (E) the water (1) + Pluronic PI05 (2) system.

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