Interaction parameter, calculation with

If the steric structures of both comonomer imits in random copolymers are similar, the melting temperature depression equation will be the same as Eq. 1, with the interaction parameter calculated with Eq. 4. For a given copolymer, the crystallizabilities of copolymer chains in dilute solution strongly depend on the chain composition. From thermodynanuc considerations, this can be explained from the fact that changes in copolymer composition alter the value of the interaction parameter de ed by Eq. 4. For copolymers with two chemically similar comonomers, xia will be very dose to xiB, ind Xab will approach zero, hi this system, one can simply use Eq. 1 with Xl = XiA Xib-... 

The above values are applicable only in the limiting case of infinite dilution. The interaction parameter varies with the volume fraction of polymer network as has been demonstrated for the PDMS-benzene system by Flory (47) and PDMS-methyl ethyl ketone, PDMS-methyl isobutyl ketone, PDMS-ethyl-n-butyl ketone, and PDMS-diisobutyl ketone by Shiomi et al. (48). Theoretically calculated and experimentally observed values of X as a function of volume fraction of polymer are given for PDMS in alkanes, aromatic hydrocarbons, and dimethyl siloxane oligomers by Gottlieb and Herskowitz (49). In the case of PDMS-alkanes, x was practically independent of the volume fraction of polymer. 

Fig 4. Polymer-solvent interaction parameter % calculated from Eq. (10) using the experimental swelling ratio as a function of inverse absolute temperature. Dashed lines represent fits to straight lines which should be obeyed in a highly swollen state. NIPA/water, O NIPA/ethanol, NIPA/n-propanol. (Reproduced with permission from Ref. 19)... 

However, for those binary polymer - solvent systems in which data of x as a function of concentration are available, it is possible to obtain the g interaction parameters directly. With the g s thus determined, it should be unnecessary to use any approximation or adjustment of binary parameters in the study of ternary systems. To provide values of g° of binary polymer - solvent systems, Masegosa et al. [6] have calculated g° for 41 polymer - solvent systems for which data of x vs. concentration were available in the literature. The values of g° calculated are collected in Table 1.2. 

Reactive compatibilization of PA/SAN blends was followed with careful TEM [Mujumdar et al., 1994a, b]. Better contrast was obtained using phosphotungstic acid than RuO. The binary interaction parameter, calculated from... 

The calculated uncertainties in A(.G° /RT will increase with the uncertainty in the interaction parameters and with increasing ionic strength. We have used the studies of [1963ALL/MCD] and the solubility investigations of many sulphate solids (see Section IX.1.3.3) to explore this effect, because the chemical system is simple, with Th(S04)3 as the dominant species. The solvent extraction data of [1963ALL/MCD], where the ionic strength varies from a very low value up to 4.5 m, were used as a first test of the impact of uncertainties in interaction parameters on the fitted values of AfG° /RT (Th(S04)3 ), as it is expected that this system will provide maximum variability in the calculated values. The values of all of the ion-interaction parameters involved in this system ate Usted in Table D-1 and the AjG° /RT values of all of the species considered in interpretation ate hsted in Table D-2. The fitted AfG° /RT (Th(S04)3 ) value was found to be -(1209.511 +0.086) when maximum values of all the ion interaction parameters, based on the uncertainties reported in Table D-1, were used and -(1209.348 + 0.088) when the minimum values were used. These compare with the value of A G° /RT (Th(S04)3 ) = -(1209.432 + 0.086) found when the mean values of the ion interaction parameters were used (see Section IX. 1.3.2). 

Fig. 19. Experimental doud points and CPC and spinodal (S) cnrves calculated with the Hory-Huggins equation, assuming that the interaction parameter decreases with conversion according to Eq. (40). Curve A represents the CPC calculated using the initial value of the interaction parameter, assumed constant (Reprinted from Polymer, M, J. Borrajo, C.C. Riccardi, R.JJ. Williams, Z.Q. Cao, J.P. Pascault, Rubber-modified cyanate esters thermodynamic analysis of phase separation, 3541-3547, Copyright (1995), with kind permission from Butterworth-Hejnemarm Journals, Elsevier Science Ltd, The Boulevard, Lan ord Lane, Kidlington 0X5 1GB, UK)...

Figure 4.9. (a) Interfacial widths as a ftinction of the interaction parameter % calculated by square gradient theory for polymer mixtures with equal chain lengths N. The dashed line is the incompatible limit of equation (4.2.10). (b) Interfacial widths normalised by the chain dimensions a N, plotted against the inverse degree of incompatibility l/(%iV). These are the same results as those shown in (a) (+, N = 3000 O, N = 1000 and X, N = 300) the solid line is the prediction of equation (4.2.10). 

The effect of polymer-polymer interactions on the miscibility and macroscopic properties of PVC/PMMA, PVC/PS, and PMMA/PS blends were studied and the miscibility of the components was characterized by the Flory-Huggins interaction parameter or by quantities related to it by Fekete et al. (Fekete et al. 2005). The comparison of interaction parameters determined by different methods indicates that PVC and PMMA are nearly miscible, while PS is immiscible either with PMMA or with PVC at all compositions. Hory-Huggins interaction parameters calculated from equihbrium methanol uptake (y jj) are plotted as a function of composition in Fig. 10.24. The negative values obtained for the PVC/PMMA blends hint at complete miscibility, although x,2 depends on composition which indicates limited miscibility. The positive interaction parameters determined for the PVC/PS and PMMA/PS blends suggest immiscibility. 

ASD including the use of in silico solubility parameter (5) calculation (Ghebremeskel et al. 2007), Flory-Huggins (F-H) interaction parameter calculation (Marsac et al. 2006b Zhao et al. 2011), drug-polymer thermodynamic phase diagrams prediction (Tian et al. 2013), crystallization inhibition with molecular dynamic calculation (Pajula et al. 2012), etc. However, in spite of their use and popularity, these theoretical methods have limitations and lack predictability, reliability, and thereby have limited utility. 

Schmitt, Kirste, and Jelenic utilized neutron scattering to determine the coil sizes and the second virial coefficients with mixtures containing two styrene/acrylonitrile copolymers, one of which was deuterated. The interaction parameter calculated... 

The Hansen solubility parameters that were calculated according to Equation 16.4 are presented in Table 16.1. With 5 values of about 17-19 (J/cm ) all plasticizing molecules were within a narrow range only the polymer seemed to have a reduced dispersive solubility parameter value reading 13.13 (J/cm )°. A better discrimination was possible by comparison of the different values of the electrostatic interaction parameter 5 with a 5 value of 11.32 (J/cm )° the pure polymer was in the same range, compared to amorphous ibuprofen [11.89 (J/cm )° ] and the hydrophilic plasticizer TEC [8.62 (J/cm )° ], thus indicating an excellent miscibility. In contrast, both the values of DBS [3.29 (J/cm )° ] and ATBC [4.57 (J/cm )° ] showed an extended lipophilic character. 

Of particular interest has been the study of the polymer configurations at the solid-liquid interface. Beginning with lattice theories, early models of polymer adsorption captured most of the features of adsorption such as the loop, train, and tail structures and the influence of the surface interaction parameter (see Refs. 57, 58, 62 for reviews of older theories). These lattice models have been expanded on in recent years using modem computational methods [63,64] and have allowed the calculation of equilibrium partitioning between a poly-... 

While the phase rule requires tliree components for an unsymmetrical tricritical point, theory can reduce this requirement to two components with a continuous variation of the interaction parameters. Lindli et al (1984) calculated a phase diagram from the van der Waals equation for binary mixtures and found (in accord with figure A2.5.13 that a tricritical point occurred at sufficiently large values of the parameter (a measure of the difference between the two components). 

A solubihty parameter of 24.5-24.7 MPa / [12.0-12.1 (cal/cm ) ] has been calculated for PVF using room temperature swelling data (69). The polymer lost solvent to evaporation more rapidly than free solvent alone when exposed to air. This was ascribed to reestabUshment of favorable dipole—dipole interactions within the polymer. Infrared spectral shifts for poly(methyl methacrylate) in PVF have been interpreted as evidence of favorable acid—base interactions involving the H from CHF units (70). This is consistent with the greater absorption of pyridine than methyl acetate despite a closer solubihty parameter match with methyl acetate. 

The solvophobic model of Hquid-phase nonideaHty takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. Eirst, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbabiHty, Henry s constant, and aqueous solubiHty (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

Figure 5. LRO-parameter S versus temperature as determined by X-ray diffraction and as calculated from resistivity measurement for CujoPtso (fit-parameter in eqn(3) A=0 7) ( ) X-rays, ( ) resistivity The curve is calculated with the Foumet model taking for the interaction energies W =720k and W2=1220k ...

TABLE II. Comparison Between Experimental EJRTC with the Value Given by the Yang-Li Quasi-Chemical Theory for Cu-Au Superlattices. Interaction Parameter, w, Calculated from Tc and the Yang-Li Theory... 

It should be born in mind, however, that the activation parameters calculated refer to the sum of several reactions, whose enthalpy and/or entropy changes may have different signs from those of the decrystalUzation proper. Specifically, the contribution to the activation parameters of the interactions that occur in the solvent system should be taken into account. Consider the energetics of association of the solvated ions with the AGU. We may employ the extra-thermodynamic quantities of transfer of single ions from aprotic to protic solvents as a model for the reaction under consideration. This use is appropriate because recent measurements (using solvatochromic indicators) have indicated that the polarity at the surface of cellulose is akin to that of aliphatic alcohols [99]. Single-ion enthalpies of transfer indicate that Li+ is more efficiently solvated by DMAc than by alcohols, hence by cellulose. That is, the equilibrium shown in Eq. 7 is endothermic ... 

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