Enthalpic interaction

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

As is known, SEC separations require interaction-free conditions. Therefore, the enthalpic contribution to the free energy term vanishes when no enthalpic interaction is postulated between analyte and sorbent ... 

As known, SEC separates molecules and particles according to their hydro-dynamic volume in solution. In an ideal case, the SEC separation is based solely on entropy changes and is not accompanied with any enthalpic processes. In real systems, however, enthalpic interactions among components of the chromatographic system often play a nonnegligible role and affect the corresponding retention volumes (Vr) of samples. This is clearly evident from the elution behavior of small molecules, which depends rather strongly on their chemical nature and on the properties of eluent used. This is the case even for... 

For these reasons, it is very important to effectively suppress the enthalpic interactions in SEC so that Benoit s plot is valid for both calibration standards and characterized polymers. This is done by choosing non (inter) active column packings, adjusting the temperature of the experiment, and applying interaction (mainly adsorption) suppressing liquids (single or mixed) as eluents. 

Measured in water (ISEC characterization based on the Ogston s model assumption is not generally reliable in alcohols owing to the occurrence of enthalpic interactions [151]). 

In principle, any type of sample can be analysed by SEC provided that it can be solubilised and that there are no enthalpic interactions between sample and packing material. By definition then, this technique cannot be carried out on vulcanisates and even unvulcanised fully compounded rubber samples can present problems due to filler-rubber interactions. The primary use of SEC is to determine the whole MWD of polymers and the various averages (number, viscosity, weight, z-average) based on a calibration curve and to allow qualitative comparisons of different samples. Many commercial polymers have a broad MWD leading to strong peak overlap in the chromatography of complex multicomponent systems. 

As has been pointed out, both entropic and enthalpic interactions affect the chromatographic behavior of macromolecules. They are adjusted to the required type of separation by selecting appropriate stationary and mobile phases. In a third mode of liquid chromatography of polymers, liquid chromatography at the critical condition (LCCC) (Entelis etal., 1985,1986 Pasch, 1997), the adsorptive interactions are fully compensated by entropic interactions. This mode is also referred to as liquid chromatography at the critical point of adsorption. Hence, TAS is equal to AH and therefore, AG becomes zero. K is 1 irrespective of molar mass and, consequently, homopolymer molecules of different molar masses coelute in one chromatographic... 

In Equation (10), Vc represents a hard-core repulsion that is entropic in nature since it is linearly dependent on temperature in the expression for energy. Repulsion is generally associated with enthalpic interactions and we can consider the effect of an enthalpic interaction. Since Vc is associated with a single Kuhn unit we consider the average enthalpy of interaction per pair-wise interaction and the number of pair-wise interactions per Kuhn unit,... 

If the backbone as well as the side chains consist of flexible units, the molecular conformation arises out of the competition of the entropic elasticity of the confined side chains and the backbone [ 153 -155]. In this case, coiling of the side chains can occur only at the expense of the stretching of the backbone. In addition to the excluded volume effects, short range enthalpic interactions may become important. This is particularly the case for densely substituted monoden-dron jacketed polymers, where the molecular conformation can be controlled by the optimum assembly of the dendrons [22-26,156]. If the brush contains io-nizable groups, the conformation and flexibility may be additionally affected by Coulomb forces depending on the ionic strength of the solvent [79,80]. 

The word vibrational, is in this case somewhat misleading, because enthalpic interactions are essentially static in nature and are purely static whenever the zeroth approximation is appropriate (see Della Giusta and Ottonello, 1993). Lastly, it must be noted that the excess term represents a reciprocal energy arising from the noncoplanarity of the four quadrilateral end-members (cf. section 3.8.7). The model of Davidson and Mukhopadhyay (1984) was reconsidered by Hirschmann (1991), who proposed an analogous treatment for (Ni,Mg,Fe)2Si04 mixtures. 

Figure 5,17 Enthalpic interactions in the various binary joins of aluminiferous garnets. calorimetric data results of interionic potential calculations. The corresponding subregular Margules interaction parameters are listed in table 5.26 (from Ottonello et al., in prep.).

Thus the retention time of D2O is caused by entropic rather than enthalpic interactions with the packing. These results confirm that the existence of micropores must be responsible for the difference in elution volume between glucose and D2O. 

Liquid Chromatography under Critical Conditions of Enthalpic Interactions.478... 

Liquid Chromatography under Limiting Conditions of Enthalpic Interactions.483... 

H results from enthalpic interactions between molecules of solute and solvent S is entropy of system T is the temperature... 

FIGURE 16.3 Dependences of the polymer retention volume on the logarithm of its molar mass M or hydrodynamic volume log M [T ] (Section 16.2.2). (a) Idealized dependence with a long linear part in absence of enthalpic interactions. Vq is the interstitial volume in the column packed with porous particles, is the total volume of liquid in the column and is the excluded molar mass, (b) log M vs. dependences for the polymer HPLC systems, in which the enthalpic interaction between macromolecules and column packing exceed entropic (exclusion) effects (1-3). Fully retained polymer molar masses are marked with an empty circle. For comparison, the ideal SEC dependence (Figure 16.3a) is shown (4). (c) log M vs. dependences for the polymer HPLC systems, in which the enthalpic interactions are present but the exclusion effects dominate (1), or in which the full (2) or partial (3,4) compensation of enthalpy and entropy appears. For comparison, the ideal SEC dependence (Figure 16.3a) is shown (5). (d) log M vs. dependences for the polymer HPLC systems, in which the enthalpic interactions affect the exclusion based courses. This leads to the enthalpy assisted SEC behavior especially in the vicinity of For comparison, the ideal SEC dependence (Eigure 16.3a) is shown (4). 

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