The entropic component of the free energy of assembly for multiparticle hydrogen-bonded aggregates is analyzed using a model based on balls connected by rigid rods or flexible strings. The entropy of assembly, ΔS, is partitioned into translational, rotational, vibrational, and conformational components. While previously reported theoretical treatments of rotational and vibrational entropies for assembly are adequate, treatments of translational entropy in solution and of conformational entropyoften the two largest components of ΔSare not. This paper provides improved estimates and illustrates the methods used to obtain them. First, a model is described for translational entropy of molecules in solution (ΔS trans(sol)); this model provides physically intuitive corrections for values of ΔS trans(sol) that are based on the Sackur−Tetrode equation. This model is combined with one for rotational entropy to estimate the difference in entropy of assembly between a 4-particle aggregate and a 6-particle one. Second, an approximate analysis of a model based on balls connected by rods or strings gives an approximate estimate of the maximum contribution of conformational entropy to the difference in free energy of assembly of flexible and of rigid molecular assemblies. This analysis, although approximate, is easily applied by all types of chemists and biochemists; it serves as a guide to the design of stable molecular aggregates, and the qualitative arguments apply generally to any form of self-assembly.
This paper examines the relationship between the composition of two-component self-assembled monolayers (SAMs) of alkanethiolates on gold and the composition of the solutions from which they were formed. The SAMs were prepared by competitive adsorption of a long-chain alkanethiol (HS(CH2)21CHs) and a short-chain alkanethiol (HS(CH2)110H) from solutions in ethanol. Under conditions in which the alkanethiolates in a SAM and the alkanethiols in solution are close to equilibrium, the relationship between the composition of the solution and the composition of the SAM suggests that the monolayer tends, thermodynamically, to exist as a single phase predominantly composed of either long-chain or short-chain thiolates. A derivation of the thermodynamic relationship between the compositions of the SAM and solution is described that includes intermolecular interactions between components in the SAM; theory and experiment agree qualitatively. This analysis concludes that, for a two-component system of alkanethiolates on gold well-equilibrated with alkanethiols in solution, a single phase is preferred at equilibrium; phase-separated, two-component monolayers of the sort extensively studied in Langmuir systems are not observed. Introduction'Mixed SAMs" on gold-self-assembled monolayers (SAMs) comprising two alkanethiolates prepared by m-chemisorption from a solution containing two alkanethiols-are useful in studying phenomena involving organic surface^.^-'^ A number of techniques can establish the average composition of a mixed SAMa2-11 X-ray photoelectron spectroscopy, XPS, can ascertain the compositionover an area thesizeofthe X-ray spot (approximately 1 mmz), and scanning electron microscopy can sometimes detect heterogeneities in composition of a SAM on the dimension of the order of 1 pm;14 phase separation has not been observed on these scales. In short, neither has the extent to which the components of a mixed SAM segregate into separate phases within a SAM been established nor has the question of the relationship between the composition of the solution used to form the SAM and its heterogeneity been addressed experimentally or theoretically. The problem is a difficult one experimentally, because there are few techniques well adapted for direct visualization of phase-separated regions with small sizes in an organic monolayer, especially on optically opaque substrates. Scanning probe microscopies (especially atomic and lateral force microscopies)17 are techniques that are applicable but only to certain types of SAMs.17-19In this paper, we investigate the phase behavior of twocomponent SAMs from both theoretical and experimental perspectives. The approach we have taken is thermodynamicto search for characteristic signatures of phase separation in the dependence of average composition on temperature, concentration, and time-rather than spectroscopic and based on imaging. We focused on the question of whether two-component SAMs form phase-separated domains. In the theoretical section, we derive a thermodynamic relationship b...
Oxidation of polyethylene with chromic acid/sulfuric acid generates a material (PE-C02H) having a high density of carboxylic acid and ketone functionalities in a thin surface layer on the polymer. This paper determines the extent of ionization of the surface and near-surface carboxylic acid groups of these materials in contact with water as a function of pH using three experimental techniques: measurement of attenuated total reflectance infrared (ATR-IR) spectra, measurement of contact angles, and direct potentiometric titration. On the basis of correlations between results obtained by these three techniques, we propose an equation relating the contact angle of an aqueous solution having a given value of pH and the extent of ionization (a;) of those carboxylic acid groups that are directly exposed to the solution. These carboxylic acid groups have broad titration curves and have C02H groups that are less acidic than soluble carboxylic acids. The initial ionization of these carboxylic acid groups occurs when the solution is approximately pH 6. The detailed structures of these oxidized polymer surface layers and the nature of the interactions between the carboxylic acid and carboxylate ions in them are still not completely defined. Salt effects on the extent of ionization a; at a particular value of pH are unexpectedly small and suggest that charge-charge interactions between carboxylate ions may not dominate the titration curves. This work demonstrates the usefulness of contact angle in following chemical changes occurring in organic functional groups on surfaces. Comparisons of wetting behavior of buffered and unbuffered solutions establishes the importance of using experimental protocols for measuring contact angles in which the reactive groups present in the interfacial region do not outnumber the reactive groups present in the small drop of dilute aqueous solution.
493 0066-426X/83/1101-0493$02.00 Annu. Rev. Phys. Chem. 1983.34:493-524. Downloaded from www.annualreviews.org by University of Massachusetts -Amherst on 10/12/12. For personal use only. Quick links to online content Further ANNUAL REVIEWS k D = 4n (DA + D B ) [ f OO eU(r)/r2 dr J-l . RA+RB 6. Annu. Rev. Phys. Chem. 1983.34:493-524. Downloaded from www.annualreviews.org by University of Massachusetts -Amherst on 10/12/12. For personal use only. DIFFUSION-CONTROLLED REACTIONS 495Several authors (4-7) have noted that the diffusion of particles toward each other is impeded by the hydrodynamic effect that arises from the need to force the solvent out of the path of mutual approach. The modification to ko from this hydrodynamic effect is (5, 6)where d(r) is the radial part of the reduced relative pair diffusion tensor �(r) 8.The tensor §"(r) contains the physical effect on the relative motion of the hydrodynamic resistance introduced by the continuum solvent. Frequently, one adopts (7) the Oseen form for §"(r) Annu. Rev. Phys. Chem. 1983.34:493-524. Downloaded from www.annualreviews.org by University of Massachusetts -Amherst on 10/12/12. For personal use only.
A calculation is presented for the effect of the hydrodynamic interaction on the diffusion-controlled rate coefficient for particles that coalesce by diffusion under the influence of an interaction potential. The hydrodynamic effect is found to make a substantial reduction in the rate compared to the Debye m~el which includes only the effects of diffusion and the forces between the reacting particles. For the case where the particles are hard spheres the reduction is 46%. For ionic species the reduction varies between 25% and 60% depending on the extent of attraction or repulsion.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.