Repulsion, steric

Steric repulsion is the term used to describe the repulsion between surfaces covered by layers of polymer or non-ionic surfactant. The 

the number of chains per unit area on the surface, np = TNA/MnA (where A is the specific surface area) 

For spherical particles of radii ax and 02 we could use the Derjaguin approximation (see for example reference 29) to calculate the potential  

There are other approximations in the literature that may be more appropriate for particular conditions.12,27,29,35 In many colloidal systems the value of 5 is 2 nm 5 10 nm and until h 2S the pair potential will be dominated by the other types of interparticle interactions, i.e. it is of short range, albeit very steep. 

Often in ceramic processing, where the surface potential is small or the double layer thickness is thin, the electrostatic repulsion is not sufficient to stabilize the colloidal suspension against coagulation. As a result another form of stabilization is needed—steric stabilization. Steric stabilization has been reviewed by two recent books, one by Napper [27] and the other by Sato and Rudi [26]. The following presentation draws heavily fiium both these books. 

There are two reasons for steric interactions (1) osmotic pressure effect due to the high concentration of chain elements in the region of the overlap as shown in Fig. 10.13, and (2) a steric effect due to the fewer possible conformations of the adsorbed molecule in the region of the overlap. These two aspects correspond to the enthalpy and entropy effects of steric stabilization. It has been found for some types of steric stabilization that increasing the temperature destabilizes the system even though for others increasing the temperature stabilizes the sys- 

FIGURE 10.13 The two aspects of steric stabilization of an adsorbed polymer 

Many attempts have been made to develop theories to predict the interaction energy between sterically stabilized particles. The details of 

State 1. /fmixing -ffpolymer/Bolvent Sphere area Z m) 

This is produced by using nonionic surfactants or polymers, for example alcohol ethoxylates, or A-B-A block copolymers PEO-PPO-PEO (where PEO refers to polyethylene oxide and PPO refers to polypropylene oxide), as illustrated in Eigure 10.11. 

The thick hydrophilic chains (PEO in water) produce repulsion as a result of two main effects [7]  

Entropic, volume restriction or elastic interaction, G p This results from the loss in configurational entropy of the chains on significant overlap. Entropy loss is unfavourable and, therefore, G j is always positive. A combination of G,. with G gives the total energy of interaction Gj (theory of steric stabilisation). 

Two approaches can be appHed to treat surfactant adsorption at the A/L and L/L interfaces [3]. In the Gibbs approach the process is treated as an equilibrium phenomenon, and it is possible to apply the Second Law of Thermodynamics. Alternately, in the Equation of state approach the surfactant film is treated as a two-dimensional layer with a surface pressure n. The Gibbs approach allows the 

At concentrations just before the break point, the slope of the y-log C curve is constant. 

Depending on the structure calculation program used, special covalent bonds such as disulfide bridges or cyclic peptide bonds have to be enforced by distance constraints. Disulfide bridges may be fixed by restraining the distance between the two sulfur atoms to 2.0-2.1 A and the two distances between the Cb and the sulfur atoms of different residues to 3.0-3.1 A [7]. 

Compounds possessing the same number and kinds of atoms and the same molecular weight (i.e. the same molecular formula) but differing in structure, are called isomers. This phenomenon is called isomerism. Five types of isomerism are recognized  

Two compounds can have different structures because of a differing arrangement of the some groups in the positional isomerism (e.g. midine vs. pseudouridine). Compounds with the same molecular formula but with different functional groups are structural isomers (e.g. D-glucose vs. D-fructose) in structural isomerism. Positional isomers and structural isomers have different chemical and physical properties because of the different arrangement of the atoms. These two types of isomers (i.e. positional isomers and structural isomers), which differ in the manner in which atoms are connected or bonded together, are also called constitutional isomers. 

Another type of isomerism is geometric isomerism. While C—C bonds rotate freely, the rotation of C=C bonds requires a larger amount of energy, therefore such a rotation seldom happens at room temperature. This inability of a double bond to rotate is known as hindered rotation, resulting in the formation of the cis (Z) isomer and the trans (E) isomer. Such pairs of geometric isomers are sometimes called double-bond diastereomers. 

For example, the configuration of L-threonine is 2S, 3R and that of its enatiomer, d-threonine is 2R, 3S. L-Allothreonine with 2S, 3S configuration is its diastereomer. It is noted that a helical chain is chiral, having right-handed (clockwise) and left-handed (counterclockwise) chirality. 

The preferred conformation will be that in which interactions between atoms on adjacent carbons are kept to a minimum. The conformations of a molecule can be analyzed in terms of three different strain factors  

While Eq. (11.11) is an exact equation, Eq. (11.12) is an approximation. Itaccurately describes the force on a single chain in the limit of very low and very high forces, but in between it is an interpolation. Other interpolations are reported in Refs [1335-1337]. 

Polymers are often used to stabilize dispersion and prevent particles from aggregation. This is due to steric repulsion. In this section, we discuss the force between surfaces coated with grafted polymer chains in a good solvent. 

When two surfaces approach each other, at some distance the polymer brushes start to overlap. The density of polymer segment increases. The increase in segment density and the resulting increase in osmotic pressure and repulsive interaction energy leads to a repulsive force [1338, 1339). 

Several equations have been proposed to describe steric repulsion [1343-1345]. We follow an argument ofde Gennes, Milner, Witten, and Cates [1346,1347]. To calculate the steric repulsion, we consider two polymer brushes with fixed grafting density. The mean distance between two grafting sites is denoted by b. Grafting density T and h are related by F = 

In equilibrium and in the absence of external forces, the net force must be zero. This leads to a brush thickness 

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The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

Two kinds of barriers are important for two-phase emulsions the electric double layer and steric repulsion from adsorbed polymers. An ionic surfactant adsorbed at the interface of an oil droplet in water orients the polar group toward the water. The counterions of the surfactant form a diffuse cloud reaching out into the continuous phase, the electric double layer. When the counterions start overlapping at the approach of two droplets, a repulsion force is experienced. The repulsion from the electric double layer is famous because it played a decisive role in the theory for colloidal stabiUty that is called DLVO, after its originators Derjaguin, Landau, Vervey, and Overbeek (14,15). The theory provided substantial progress in the understanding of colloidal stabihty, and its treatment dominated the colloid science Hterature for several decades. 

The //NMR spectrum (Fig. 2.19) displays anAB system for the protons adjacent to this bond the coupling constant = 72 Hz. From this can be deduced first that the dihedral angle 9 between the C7/bonds is about 180°, second that conformer 14b with minimised steric repulsion between the substituents predominates and third that there is restricted rotation around this CC bond. 

Separation of enantiomers by physical or chemical methods requires the use of a chiral material, reagent, or catalyst. Both natural materials, such as polysaccharides and proteins, and solids that have been synthetically modified to incorporate chiral structures have been developed for use in separation of enantiomers by HPLC. The use of a chiral stationary phase makes the interactions between the two enantiomers with the adsorbent nonidentical and thus establishes a different rate of elution through the column. The interactions typically include hydrogen bonding, dipolar interactions, and n-n interactions. These attractive interactions may be disturbed by steric repulsions, and frequently the basis of enantioselectivity is a better steric fit for one of the two enantiomers. ... 

The dependence on steric bulk is attributed to the steric requirements imposed by the bulky trimefliylamine leaving group. In the transition state for anti elimination, steric repulsion is increased as R and increase in size. When the repulsion is sufficiently large, the transition state for syn elimination is preferred. 

An interesting and useful property of enamines of 2-alkylcyclohexanones is the fact that there is a substantial preference for the less substituted isomer to be formed. This tendency is especially pronounced for enamines derived from cyclic secondaiy amines such as pyrrolidine. This preference can be traced to a strain effect called A or allylic strain (see Section 3.3). In order to accommodate conjugation between the nitrogen lone pair and the carbon-carbon double bond, the nitrogen substituent must be coplanar with the double bond. This creates a steric repulsion when the enamine bears a p substituent and leads to a... 

One of the C(15) epimeric thio esters (B) cyclizes more slowly than the other (by a factor of 03. 15) due to steric repulsions involving the methyl group at C(15). After lactonization, the uncyclized diastereomer was recovered and used for the synthesis as following. 

Finally, we assume that the fields 4>, p, and u vary slowly on the length scale of the lattice constant (the size of the molecules) and introduce continuous approximation for the thermodynamical-potential density. In the lattice model the only interactions between the amphiphiles are the steric repulsions provided by the lattice structure. The lattice structure does not allow for changes of the orientation of surfactant for distances smaller than the lattice constant. To assure similar property within the mesoscopic description, we add to the grand-thermodynamical potential a term propor-tional to (V u) - -(V x u) [15], so that the correlation length for the orientational order is equal to the size of the molecules. 

R, = CjHj, Rj, R3 = (0112)4] (45). Even the possibility of stabilization of the double bond by conjugation with an aromatic ring was not enough to overcome the steric repulsions. The enamine formed is probably an equilibrium product 46). 

In deoxyhemoglobin, histidine F8 is liganded to the heme iron ion, but steric constraints force the Fe His-N bond to be tilted about 8° from the perpendicular to the plane of the heme. Steric repulsion between histidine F8 and the nitrogen atoms of the porphyrin ring system, combined with electrostatic repulsions between the electrons of Fe and the porphyrin 77-electrons, forces the iron atom to lie out of the porphyrin plane by about 0.06 nm. Changes in... 

Transition-state stabilization in chymotrypsin also involves the side chains of the substrate. The side chain of the departing amine product forms stronger interactions with the enzyme upon formation of the tetrahedral intermediate. When the tetrahedral intermediate breaks down (Figure 16.24d and e), steric repulsion between the product amine group and the carbonyl group of the acyl-enzyme intermediate leads to departure of the amine product. 

Steric repulsion occurs when two atoms with filled valence shells are forced so close together that their electron clouds must occupy, in part, the same region of space. 

Alkanes prefer structures that stagger bonds on adjacent tetrahedral carbons (see Chapter 5, Problem 1). However, steric repulsion can affect the relative energies of staggered conformations. 

Which conformation is more stable, anti or gauchel What evidence is there for steric repulsion between methyl groups in the gauche conformation (Hint Look for distortions in the CCC bond angles as a function of conformation.)... 

Internal rotation in isooctane (2,2,4-trimethylpentane) creates a large number of staggered conformations. However, only rotation about the C3-C4 bond produces conformations with different structures. Plot the energy of isooctane (vertical axis) vs. HCCCtBu torsion angle, i.e., about the C3-C4 bond (horizontal axis). How many minimum energy structures are there Are they all fully staggered Draw Newman projections that show the conformation of these structures. How does steric repulsion affect isooctane conformation ... 

Internal rotation in cycloalkanes is restricted by the need to maintain bonding between adjacent ring atoms. Aside from this restriction, though, cycloalkanes obey the same structural rules as alkanes staggered conformations that tninimize steric repulsion are preferred. 

Try to explain the conformational preference in terms of steric repulsion. Which ring atom(s) in the higher-energy conformer approach the CH3 group most closely (Make sure that you find all significant nonbonded interactions.) Which of these interactions are absent in the lower-energy conformer Can interactions that appear in both conformers account for the conformational preference ... 

The conformation of alkylcyclohexanes is determined largely by steric repulsion (see Chapter 5, Problems 6 and 7). More polar substituents may show different conformational preferences due to a combination of steric and electronic factors. 

Compare energies for both diaxial and diequatorial chair conformers of trans-2-fluoromethyIcyclohexane (X = Me). Which conformer is preferred Examine a space-filling model of each conformer. Which group is largest methyl, fluorine, or hydrogen Which is smallest Does the preferred conformer minimize steric repulsion Explain. 

CH3I should approach the enolate from the direction that simultaneously allows its optimum overlap with the electron-donor orbital on the enolate (this is the highest-occupied molecular orbital or HOMO), and minimizes its steric repulsion with the enolate. Examine the HOMO of enolate A. Is it more heavily concentrated on the same side of the six-membered ring as the bridgehead methyl group, on the opposite side, or is it equally concentrated on the two sides A map of the HOMO on the electron density surface (a HOMO map ) provides a clearer indication, as this also provides a measure of steric requirements. Identify the direction of attack that maximizes orbital overlap and minimizes steric repulsion, and predict the major product of each reaction. Do your predictions agree with the thermodynamic preferences Repeat your analysis for enolate B, leading to product B1 nd product B2. 

The parameter redundancy is also the reason that care should be exercised when trying to decompose energy differences into individual terms. Although it may be possible to rationalize the preference of one conformation over another by for example increased steric repulsion between certain atom pairs, this is intimately related to the chosen functional form for the non-bonded energy, and the balance between this and the angle bend/torsional terms. The rotational banier in ethane, for example, may be reproduced solely by an HCCH torsional energy term, solely by an H-H van der Waals repulsion or solely by H-H electrostatic repulsion. Different force fields will have (slightly) different balances of these terms, and while one force field may contribute a conformational difference primarily to steric interactions, another may have the... 

For the 2-1-2 pathway the FMO sum becomes (ab — ac) = a b — c) while for the 4 -I- 2 reaction it is (ab-I-ab) — a (2b). As (2b) > (b — c), it is clear that the 4 + 2 reaction has the largest stabilization, and therefore increases least in energy in the initial stages of the reaction (eq. (15.1), remembering that the steric repulsion will cause a net increase in energy). Consequently the 4 - - 2 reaction should have the lowest activation energy, and therefore occur easier than the 2-1-2. This is indeed what is observed, the Diels-Alder reaction occurs readily, but cyclobutane formation is not observed between non-polar dienes and dieneophiles. 

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