Mixtures entropic part

Positive values of x necessarily lead to incompatibility. Since the entropic part, xSi appears to be mostly positive, one may also state that no polymer mixtures exist with a positive heat of mixing. 

Fig. 15 Enthalpic and entropic parts of FH parameters for the three dPB/PS blends versus pressure. In all cases a decrease with pressure is found. The lowest numbers are found for the PB copolymer mixtures which saturates above 100 MPa...

Referring to the analysis of kinetic barriers that contribute to the differential rates, outlined above, it would appear that enantioselectivity may not reside in any single part of the kinetic scheme. In fact, analysis of the distribution of entropic and enthalpic contributions to the enantioselectivity of CaLB in mixtures of organic solvents showed that the gradual replacement of one organic solvent with the other may lead to a switch from one state to another [145]. More information on the response of individual steps in the kinetic scheme to a change of solvent is needed to arrive at a conclusive answer. 

The N-(bicycloalkenyl)nitrone (37) afforded the tetracyclic isoxazolidine (38) in 67% yield none of the regioisomeric isoxazolidine was observed (Scheme 9).17 The authors attributed this to non-bonded C—H interactions as shown, but the observed isoxazolidine was also entropically favored, forming via a six-membered, as opposed to a seven-membered, carbocyclic transition state. The N-(bicycloalkenyl)ni-trone formed from (39) and furfural cyclized in 45% yield predominantly to the tetracyclic product (40b), but some (41b) was also produced (95 5 ratio).18 Reaction of (39) and formaldehyde gave a mixture of (40a) and (41a) (62 38 ratio). The authors attribute the somewhat higher regioselectivity for (40b) in part to non-bonded interaction of the 2-furyl substituted methylene with the C-8 endocyclic C—H bond. 

The contrast of this work compared to findings for mixtures of small molecule liquid crystals ( ) suggests that entropy plays an important part in determining miscibility in liquid crystal systems. The entropic effect could conceivably enter in two different ways. 

The opposite case where the energy dominates is found at r=0 K. because the entropic contribution vanishes. The free energy only has an energetic part given, for example, by Eq. (4.22) for regular mixtures. Differentiating Eq. (4.22) twice with respect to composition determines whether the blend is locally stable at 0 K... 

Although a modelling of a liquid polymer mixture on a lattice may first look rather artificial, it makes sense because it retains the important aspects of both the entropic and enthalpic part of A mix- In recent years, lattice models have gained a renewed importance as a concept which is suitable for computer simulations. Numerical investigations make it possible to check and assess the validity range of the Flory-Huggins treatment. In fact, limitations exist and, as analytical calculations are difficult, simulations are very helpful and important. We shall present one example in a later section. 

The lack of a center of symmetry in the monomer repeat imit structure of PA6 imparts a directionality to the PA6 chains. Consequently, PA6 can form the a-crystalline, planar hydrogen bonded sheet structure only between antiparallel chains. Parallel chains, on the other hand, form a 7-crystalline, pleated sheet structure in which the chains assume a twisted helix conformation to permit lull H-bonding. Due to these symmetry and entropic restrictions, PA6 is somewhat less crystalline and less ordered, usually containing a mixture of a and 7-crystalline forms in the injection molded parts. As a consequence of these crystallinity and morphology differences, PA6 is intrinsically more ductile than PA66, since it is easier to deform a less ordered polymer phase. 

Although a modeling of a liquid pol3uner mixture on a lattice may at first look rather artificial, it makes sense because it retains the important aspects of both the entropic and enthalpic parts of Af/mix- In recent years, lattice... 

In the SCLF model, adsorption is depicted as the result of nonCoulombic interactions between the solute and solvent molecules and the electrostatic surface potential. The solution is divided into lattice sites which are arrayed in layers parallel to the surface. The equilibrium distribution of solute molecules between the solution and surface is determined from the partition function, Q, for a solution mixture [50, 52, 55] constituted of an entropic, and an energetic part, U, of general form [e.g., see Eq. (8) in Ref 53] ... 

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