Molecules packing density

The secondary and tertiary structures of myoglobin and ribonuclease A illustrate the importance of packing in tertiary structures. Secondary structures pack closely to one another and also intercalate with (insert between) extended polypeptide chains. If the sum of the van der Waals volumes of a protein s constituent amino acids is divided by the volume occupied by the protein, packing densities of 0.72 to 0.77 are typically obtained. This means that, even with close packing, approximately 25% of the total volume of a protein is not occupied by protein atoms. Nearly all of this space is in the form of very small cavities. Cavities the size of water molecules or larger do occasionally occur, but they make up only a small fraction of the total protein volume. It is likely that such cavities provide flexibility for proteins and facilitate conformation changes and a wide range of protein dynamics (discussed later). 

AFM is used in the surface analysis. Figure 16 is the AFM topography of the monolayer and the multilayer L-B films. It shows that the monolayer L-B film is well packed and highly ordered on the mica surface. The surface of the monolayer film (shown in Fig. 16(a)) has a higher packing density than that of the four-layer L-B film (shown in Fig. 16(b)). This is because the molecules form the different structures in the monolayer film from those in four-layer... 

Polyethylene, a thermoplastic, is the largest selling plastic material. LDPE is a branched polyethylene whose branches prevent close packing and gives low density. HDPE is polyethylene that has essentially no branching, so the molecules pack very well, which leads to high density and high crystallinity. LLDPE is actually a copolymer prepared at low temperature and low pressure from a mixture of ethylene and about 10% of a C4-C8 olefin. 

N Is the number of molecules per unit volume (packing density factor), fv Is a Lorentz local field correction at frequency v(fv= [(nv)2 + 2]/3, v = u) or 2u). Although generally admitted, this type of local field correction Is an approximation vdilch certainly deserves further Investigation. IJK (resp Ijk) are axis denominations of the crystalline (resp. molecular) reference frames, n(g) Is the number of equivalent positions In the unit cell for the crystal point symmetry group g bjjj, crystalline nonlinearity per molecule, has been recently Introduced 0.4) to get general expressions, lndependant of the actual number of molecules within the unit cell (possibly a (sub) multiple of n(g)). 

The structure of ice is shown in the diagram. The crystal structure of ice is essentially tetrahedral. When water melts, the hydrogen bonds are progressively broken. The molecules pack closer together and so an initial reduction in volume of the liquid occurs before the usual expansion effect from raising the temperature is observed. Water, therefore, has its maximum density at 4°C. 

The interlayer region of LDHs can provide a novel environment for photochemical reactions of guest molecules [201-204]. For example, Takagi et al. reported that the controlled photodimerization of a variety of unsaturated carboxylate species intercalated in the interlayer galleries of Mg/Al LDH could occur between the layers [203]. Syn head-to-head cyclodimers were selectively formed in the irradiation of intercalated cinnamate ions, whereas two isomers of syn head-to-head and syn head-to-taU cyclodimers were formed for the case of phenylethenylbenzoates. The product selectivity was shown to be controlled by the Mg/Al ratio of the host LDH, and hence the packing density of the anions in the interlayer region [204]. 

Natural biological membranes consist of lipid bilayers, which typically comprise a complex mixture of phospholipids and sterol, along with embedded or surface associated proteins. The sterol cholesterol is an important component of animal cell membranes, which may consist of up to 50 mol% cholesterol. As cholesterol can significantly modify the bilayer physical properties, such as acyl-chain orientational order, model membranes containing cholesterol have been studied extensively. Spectroscopic and diffraction experiments reveal that cholesterol in a lipid-crystalline bilayer increases the orientational order of the lipid acyl-chains without substantially restricting the mobility of the lipid molecules. Cholesterol thickens a liquid-crystalline bilayer and increases the packing density of lipid acyl-chains in the plane of the bilayer in a way that has been referred to as a condensing effect. 

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