Conformational contribution to the entropy of melting. II. Comparison between theory and experiment

Abstract

Experimental and theoretical values of the conformational entropy contribution ΔSc to the melting entropy of linear hydrocarbons agree fairly well; however, the chain model in which each bond has three possible conformations (g+, g−, and t) seems to be probably oversimplified. However, ratios of ΔSc to the actual number of bonds, which are effective in increasing the number of conformations, increase theoretically with chain length, whereas experimental values decrease. This latter behavior can be due to the increasing intra- and intermolecular packing difficulties as the hydrocarbon chain length increases.

Using a Convenient, Quantitative Model for Torsional Entropy To Establish Qualitative Trends for Molecular Processes That Restrict Conformational Freedom

“…The conformational entropy for such straight chain alkanes (containing N carbons) have been estimated on the basis of the experimental entropy of melting (Δ S melt ) and are in the range Δ S melt /( N − 2) ∼6.65−7.11 J mol -1 K -1 per torsion; these values are approximately the same as those calculated using eq 1. ,,,,,, Experimentally, there is only a small dependence of the value of Δ S melt /( N − 2) on chain length N : this observation is consistent with our finding in this work that the values of S tor within a straight chain alkane are relatively independent of one another. ,,,,,, …”

“…We believe that our model for Δ S tor will be useful in estimating the entropic components to the free energy for molecular processes that involve a change in the degree of restriction of single bonds with low torsional barriers. Examples of such processes (Figure ) may include binding of flexible substrates to enzymes, the chelate effect, reactions with enhanced rates due to intramolecularity, , cyclizations of saturated linear chains, adsorption of flexible, long-chain alkanes onto metallic surfaces to form a 2-dimensional monolayer, melting of solids into liquids and subliming of solids into gases, , transfer of flexible hydrophobic molecules from water into organic solvent, , self-assembly of multiple flexible particles to make a stable aggregate in solution, , folding of proteins, − interactions of divalent antibodies with polyvalent surfaces, binding of ligands (especially those that are polyvalent) to receptors, − and the interaction of a protein with a polymeric, well-hydrated protein-resistant surface. −

1 Illustrations of some synthetic and natural processes in which torsions are restricted. See text for references.

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Decomposition of entropy and enthalpy for the melting transition of polyethylene

“…(For convenience, we will not write the angular brackets for changes such as AUR.) Similarly, intermolecular van der Waals energies, UvdW, are also well-defined sums over states (Uvdw) = S(Uvdw)aPs (8) where UvdW is calculated for each state s in the usual way. Even though we do not attempt, in this paper, to perform the sums over states from first principles, it is clear that the quantities AU¡ have a precise and well-defined meaning in statistical mechanics.…”

A Critical Study of the Entropy−Volume Relation of Chain Molecules in the Fluid State: Computer Simulation of n-Undecane and Comparison with Experimental PVT Data

“…In this work, we have just concentrated in investigating the volume dependence of γ in the liquid state. In treating the transition entropy of real systems, contributions from the so-called communal entropy as well as other residual entropies are often considered by introducing an extra term Δ S d in eq 1: ,, …”

“…The entropy separation according to eqs 1 and 2 is a hypothetical process assuming that the volume of the isotropic fluid may be compressed to that of the solid state without affecting the configurational part of the entropy of chain molecules . The validity of such an assumption has been questioned by several authors. − Wunderlich et al pointed out that the volume dependence of γ during the compression from the liquid to the solid volume may not be negligible and thereby leads to a significant underestimate of the Δ S V term. They proposed to adopt an integration form such as to replace eq 1.…”