Infrared studies of single crystals of polycaprolactam

Infrared studies of the α-crystalline form of polycaprolactam (nylon 6) have confirmed the assignment of the 1288 and 1210-cm^?1 bands to a unique fold conformation. The γ-crystalline phase has a band at 1212 cm^?1 which overlaps the 1210-cm^?1 fold band in samples containing both α and γ phases. The 1288-cm^?1 band was, therefore, used to monitor regular fold content. No unique fold bands were detected in the γ form. Irregular folds present in solution-grown crystals regularize to the unique fold conformation upon annealing. Crystals which originally exhibit slight differences in regular folding as a result of different crystallization history have similar amounts of regular folds upon annealing at 220°C. Crystals grown from solutions of very dilute concentrations of polymer have different amounts of regular folding. The annealing behavior of crystals prepared from two different solution concentrations reflect the processes of regularization and long period increase.     

Infrared studies of chain folding in polymers. v. polyhexamethylene adipamide

Systematic infrared studies of a series of polyhexamethylene adipamides (nylon 66) have resulted in the assignment of two bands to the regularly folded polymer chain. Utilizing this assignment and long-period measurements by small-angle X-ray diffraction, a method has been developed to compare the amount of regular chain folding in solution-crystallized samples precipitated at different temperatures. At high supercoolings in solution, only 60% of the chain folding which occurs has a regular structure. Annealing of the solution-crystallized samples not only produced a longer fold period but also regularized the folds. Melt-crystallized samples when annealed do not show much increase in fold period or regularization of the folds. Glass-crystallized samples show a rapid initial increase with time at a particular temperature in long period and regular folding. For the glass-crystallized samples crystallized at different temperatures for the same period of time, higher temperatures of crystallization produce longer fold periods and greater fractions of regular folds. The infrared fold bands disappear when samples consisting of regular folds are deformed but reappear after annealing.     

Chain folding and the structure of nylon 6.6 spherulites

Following the assignment of the 1329 and 1224 cm^?1 infrared bands to chain-folded conformations in nylon 6.6 by Koenig et al. examination of the infrared spectra of positively birefringent and negatively birefringent spherulitic films has been made. The spectra indicate extensive regular folding in negative spherulites but fewer folds or less regular folding in the positive spherulite structure.

The assignment of the infrared fold bands to modes of vibration of the repeat unit is discussed with reference to the spectra of films with varying extents of N deuteration (normal 6.6, disordered regions deuterated, N deutero 6.6, disordered regions hydrogenated).

Electron micrographs of negative spherulites are analyzed with the infrared and previous evidence. We suggest they are built up of single-crystal lamellae of 0.2 to 0.3 μ lateral dimensions packed with a preferential orientation of the lamellae planes parallel to the radial direction but otherwise randomly oriented.     

Infrared studies of chain folding in polymers. X. polycaprolactam

The 1210-, 1233-, and 1288—cm^?1 infrared bands in the α form of nylon 6 are shown to result from a unique conformation in a tightly folded chain with adjacent reentry. The assignment of the 1210- and 1288-cm^?1 bands to motions of a gauche nitrogen-methylene group in the fold and the 1233-cm^?1 band to motions of a gauche carboxyl-methylene group in the fold is supported by the infrared studies of the α form of nylon 6, the γ form of nylon 6, poly-D(-)β-methyl- ? -caproamide (PBCA), and the high- and low-temperature forms of the cyclic dimer of nylon 6. The γ- form of nylon 6 and PBCA do not exhibit a unique conformation in the fold. The 1198-cm^?1 band can be assigned to the trans conformation of the amide group which exists in the normal planar zigzag conformation in the α-form crystal. A mechanism for the α to γ iodine-induced transition in nylon 6 is proposed showing the role of the fold in maintaining a minimum of molecular disordering during the transformation.     

Mechanisms for regularization of chain folds during annealing of polyhexamethylene adipamide

The regular fold content of polyhexamethylene adipamide depends on the initial crystallization conditions, the degree of orientation, and the annealing time and temperature. At low annealing temperatures, the regular fold content increases linearly with crystallinity and arises from lamellar crystallization of isolated amorphous or interlamellar regions. At intermediate annealing temperatures, the increase in regular fold content greatly exceeds the crystallinity increase. The excessive increase in folds in this temperature range arises from regularization of loose loops and melting and recrystallization from extended to more folded type of crystals. At the higher annealing temperature, the crystallinity shows an increase relative to the fold content, and this implies that the increase in fold period occurs at the expense of folding.     

Chain conformations on the surface of polyethylene single crystals

New conformations for the shortest folds of polyethylene single crystals were determined from the principles: (1) the conformations of polymethylene chains are basically determined by the rotational isomeric approximation, (2) the crystal part is deformed where it is connected with the fold part, and (3) the conformation of the fold must be determined as the minimum of surface energy, not of conformation energy. It was shown that the surface energy, assuming the crystal state as the reference state, was composed of four terms: (i) the deformation energy of the crystal part, (ii) the sublimation energy of the fold part, (iii) the conformation energy of the fold part, and (iv) the interaction energy between folds. The conformations of the shortest fold were basically (GTGGTGGG) for (110)-folds and (G'G'TTGG) for (200)-folds. The setting angles of all the chains in the crystal part are rotated from their normal angle (41°) to 41 + a° at the boundary between the two parts. The fold part is deformed so as to fit in with the deformed boundary of the crystal part. The conformations with minimum surface energy were obtained at a = 30° for both (110)-and (200)-folds. Their surface energies were about 16 kcal/mole of fold (300 erg/cm2). The surface energies, assuming the liquid state as the reference state, were about 7 kcal/mole of fold (130 erg/cm²).     

Fold amplification rates and dominant wavelength selection in multilayer stacks

A combination of thin- and thick-plate theories, and finite element models is used to systematically analyze folding in multilayer stacks. We show that if the interlayer spacing is large, individual layers fold as single layers, if the spacing is small the entire stack folds as one effective single layer. In between, a third folding mode exists that is characterised by a dominant wavelength that scales with n ^1/3, irrespective of total number of layers, n. The maximum growth rates in the true multilayer-folding mode are higher than the corresponding single layer growth rates, increase with n and are bounded by a saturation value that is directly proportional to the viscosity contrast. This growth rate saturation as well as the applicability of the true multilayer-folding mode with respect to interlayer spacing can be explained by the normal and inverse contact strain theory. The true multilayer-folding mode is expected to be the most frequent mode in nature, because it exhibits the highest growth rates and has a relatively large applicability range with respect to interlayer spacing. The increased growth rates in multilayer folding are especially important for systems where the corresponding single layer values are not sufficient to drive the folding instability, such as folding in low-viscosity contrast layers and detachment folding.     

Three-dimensional folding of the triangular lattice

We study the folding of the regular triangular lattice in three-dimensional embedding space, a model for the crumpling of polymerised membranes. We consider a discrete model, where folds are either planar or form the angles of a regular octahedron. These “octahedral” folding rules correspond simply to a discretisation of the 3d embedding space as a Face Centred Cubic lattice. The model is shown to be equivalent to a 96-vertex model on the triangular lattice. The folding entropy per triangle ln q_3d is evaluated numerically to be q_3d = 1.43(1). Various exact bounds on q_3d are derived.     

Dynamics of folding in semiflexible filaments

The dynamics of a single semiflexible filament under the action of a compressing force is simulated. We find that the filament folds asymmetrically with a folding length which depends only on the bending stiffness kappa and the applied force f. It is shown that this behavior can be attributed to the exponentially falling tension profile in the filament. While the folding time tau(0) depends on the initial configuration, the distance moved by the terminal point of the filament and the length of the fold scales as tau(1/2) at tau>tau(0) and is independent of the initial configuration.     

Analysis of protein folds using protein contact networks

Proteins are important biomolecules, which perform diverse structural and functional roles in living systems. Starting from a linear chain of amino acids, proteins fold to different secondary structures, which then fold through short- and long-range interactions to give rise to the final three-dimensional shapes useful to carry out the biophysical and biochemical functions. Proteins are defined as having a common ‘fold’ if they have major secondary structural elements with same topological connections. It is known that folding mechanisms are largely determined by a protein’s topology rather than its interatomic interactions. The native state protein structures can, thus, be modelled, using a graph-theoretical approach, as coarse-grained networks of amino acid residues as ‘nodes’ and the inter-residue interactions/contacts as ‘links’. Using the network representation of protein structures and their 2D contact maps, we have identified the conserved contact patterns (groups of contacts) representing two typical folds — the EF-hand and the ubiquitin-like folds. Our results suggest that this direct and computationally simple methodology can be used to infer about the presence of specific folds from the protein’s contact map alone.      

Fractal protein structure revisited: Topological, kinetic and thermodynamic relationships

The present work explored the definitions and calculations of fractal dimensions in protein structures and the corresponding relationships with the protein class, secondary structure contents, fold type as well as kinetic and thermodynamic parameters like the folding and unfolding rate, the folding–unfolding free energy and others. The results showed a positive correlation of some fractal exponents with the kinetic and thermodynamic variables even considering the effect of the protein length. On the other hand the influences of secondary structures types, especially the turn conformation are significant as well as the fractal exponent profiles according to class and fold types.     

Distance distributions and dynamics of a zinc finger peptide from fluorescence resonance energy transfer measurements

Time-resolved fluorescence resonance energy transfer (FRET) measurements were used to measure distance distributions and intramolecular dynamics (site-to-site diffusion) of a 28-residue single-domain zinc finger peptide in the absence and presence of zinc ion. Energy transfer was measured between TRP₁₄ and a N-terminal DNS group. As expected, the TRP-to-DNS distance distribution for zinc-bound peptide is shorter and narrower (R _av=11.2 Å,hw=2.8 Å) than the metal-free peptide (R _av=20.1 Å,hw=14.5 Å). The degree of mutual donor-to-acceptor diffusion (D) was also determined for these distributions. For zinc-bound peptide there is no detectible diffusion (D0.2 Ų/ns), whereas for metal-free peptide a considerable amount of motion is occurring between the donor and the acceptor (D=12 Ų/ns). These results indicate that the zinc-bound peptide folds into a unique, well-defined conformation, whereas the metal-free conformation is flexible and rapidly changing. The absence of detectible mutual site-to-site diffusion between the donor and the acceptor in the metal-bound zinc finger peptide indicates that intramolecular motion is essentially frozen out, on the FRET time scale, as a consequence of zinc coordination.Dedicated to the memory of Barbara D. Wells.     

A model for vocal fold vibratory motion, contact area, and the electroglottogram

The electroglottogram (EGG) has been conjectured to be related to the area of contact between the vocal folds. This hypothesis has been substantiated only partially via direct and indirect observations. In this paper, a simple model of vocal fold vibratory motion is used to estimate the vocal fold contact area as a function of time. This model employs a limited number of vocal fold vibratory features extracted from ultra high-speed laryngeal films. These characteristics include the opening and closing vocal fold angles and the lag (phase difference) between the upper and lower vocal fold margins. The electroglottogram is simulated using the contact area, and the EGG waveforms are compared to measured EGGs for normal male voices producing both modal and pulse register tones. The model also predicts EGG waveforms for vocal fold vibration associated with a nodule or polyp.     

Finite amplitude folding of single layers: elastica,bifurcation and structural softening

The amplification of viscous single-layer folds, from infinitesimal amplitudes up to finite amplitudes and large strains, is investigated analytically. Analytical solutions for finite amplitude folding of viscous layers valid for large viscosity contrasts and for post-buckling of elastic columns are shown to be identical. The failure of the classical, exponential amplification solution for folding is quantified using a nonlinear amplification equation similar to the Landau equation. The evolution of fold amplitude–strain for single layers with different initial amplitudes and viscosity contrasts essentially depends on a single parameter rather than three parameters as commonly assumed (strain, initial amplitude and viscosity contrast). This single parameter is constructed by scaling the strain with the crossover strain, which is the specific value of strain at which the linear solutions fail. Scaling the strain with the crossover strain yields a collapse of all amplitude evolution paths for different initial amplitudes and viscosity contrasts onto a single amplification path. Analytical solutions for the evolution of the layer-parallel deviatoric stress within the layer during folding are presented showing a decrease of the layer-parallel deviatoric stress with increasing fold amplitude. All stress–amplitude evolution paths for different initial amplitudes and viscosity contrasts can be collapsed onto a single stress–amplitude evolution path, if the amplitude is scaled by the crossover amplitude. The decrease in stress is proportional to a decrease in effective viscosity of the layer during folding. This decrease in effective viscosity represents structural softening, because the true, Newtonian viscosity of the layer remains constant.     

Effects of Surface Dipole Lengths on Evaporation of Tiny Water Aggregation

Using molecular dynamics simulation, we compared evaporation behavior of a tiny amount of water molecules adsorbed on solid surfaces with different dipole lengths, including surface dipole lengths of 1 fold, 2 folds, 4 folds, 6 folds and 8 folds of 0.14 nm and different charges from 0.1e to 0.9e. Surfaces with short dipole lengths (1-fold system) can always maintain hydrophobic character and the evaporation speeds are not influenced, whether the surface charges are enhanced or weakened; but when surface dipole lengths get to 8 folds, surfaces become more hydrophilic as the surface charge increases, and the evaporation speeds increase gradually and monotonically. By tuning dipole lengths from 1-fold to 8-fold systems, we confirmed non-monotonic variation of the evaporation flux (first increases, then decreases) in 4 fold system with charges (0.1e-0.7e), reported in our previous paper [S. Wang, et al., J. Phys. Chem. B 116 (2012) 13863], and also show the process from the enhancement of this unexpected non-monotonic variation to its vanishment with surface dipole lengths increasing. Herein, we demonstrated two key factors to influence the evaporation flux of a tiny amount of water molecules adsorbed on solid surfaces: the exposed surficial area of water aggregation from where the water molecules can evaporate directly and the attraction potential from the substrate hindering the evaporation. In addition, more interestingly, we showed extra steric effect of surface dipoles on further increase of evaporation flux for 2-folds, 4-folds, 6-folds and 8-folds systems with charges around larger than 0.7e. (The steric effect is first reported by parts of our authors [C. Wang, et al., Sci. Rep. 2 (2012) 358]). This study presents a complete physical picture of the influence of surface dipole lengths on the evaporation behavior of the adsorbed tiny amount of water.     

Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such a surface may model a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry through folding along portions of meridians. For the thinnest shells, a direct transition from the spherical conformation to the folded one can be observed. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of Poisson's ratio. In the folded conformation, the number of folds and inner pressure are investigated, allowing us to infer shell features from mere observation and/or knowledge of external constraints.     

Laser Doppler Measurements of the Vocal Fold Blood Micro-Circulation

The authors have developed a laser Doppler method, referred to as LDF+LS (laser Doppler flowmetry by laryngostereometry), for measuring the vocal fold micro-circulation. The vocal folds of 103 patients were examined during general anesthesia. A laser Doppler probe was placed on defined positions at the vocal fold edge: midmembranous position (MP), 2 mm and 4 mm behind, and 1 mm anterior to MP. Three parameters were derived, ie, the concentration (CMBC) and velocity (V) of moving blood cells, and the product of both resulting in perfusion: P = CMBCxV. The results of 53 subjects with normal vocal fold status showed that the V at MP was significantly lower than 2 mm behind MP (P < 0.05). Men had significantly higher velocity than women (P < 0.05). Subjects older than 65 years had higher perfusion and CMBC as compared with younger subjects (P < 0.01). Smokers with normal vocal folds had higher velocity than non-smokers (P < 0.05). Measurements of healthy vocal folds were compared with benign vocal fold pathology. Vocal fold polyps had significantly higher perfusion than normal vocal folds (P < 0.01). In conclusion, the laser Doppler measurement is a sensitive tool estimating superficial blood flow in both normal and pathological vocal folds. The blood flow in normals differs with respect to gender and age probably due to variations in micro-circulation of the mucosa and lamina propria. Vocal fold pathology and external factors such as smoking result in blood flow changes.     

Vibration in a self-oscillating vocal fold model with left-right asymmetry in body-layer stiffness

This study compares the phonatory behavior of an asymmetric vocal fold model to that of each individual vocal fold model in a hemi-configuration. Although phonation frequencies of the two folds in hemi-configurations had a ratio close to 1:3, a subharmonic synchronization between the two folds was not observed in the asymmetric model. Instead, the vibratory behavior was dominated by the dynamics of one fold only, and the other fold was enslaved to vibrate at the same frequency. Increasing subglottal pressure induced a shift in relative dominance between the two folds, leading to abrupt changes in both vibratory pattern and frequency.     

Voice source characteristics in Mongolian "throat singing" studied with high-speed imaging technique, acoustic spectra, and inverse filtering.

Mongolian "throat singing" can be performed in different modes. In Mongolia, the bass-type is called Kargyraa. The voice source in bass-type throat singing was studied in one male singer. The subject alternated between modal voice and the throat singing mode. Vocal fold vibrations were observed with high-speed photography, using a computerized recording system. The spectral characteristics of the sound signal were analyzed. Kymographic image data were compared to the sound signal and flow inverse filtering data from the same singer were obtained on a separate occasion. It was found that the vocal folds vibrated at the same frequency throughout both modes of singing. During throat singing the ventricular folds vibrated with complete but short closures at half the frequency of the true vocal folds, covering every second vocal fold closure. Kymographic data confirmed the findings. The spectrum contained added subharmonics compared to modal voice. In the inverse filtered signal the amplitude of every second airflow pulse was considerably lowered. The ventricular folds appeared to modulate the sound by reducing the glottal flow of every other vocal fold vibratory cycle.     

The biomechanics of the medialization laryngoplasty(thyroplasty type 1) in an ex vivo canine model

The biomechanics of medialization laryngoplasty are not well understood. An excised canine larynx model was used to test the effects of various sized silicon implants. The vocal fold length, position, and tension were measured. Medialization laryngoplasty did not affect vocal fold length. At the mid-membranous vocal fold, larger shims resulted in greater medialization and tension. Medialization laryngoplasty neither medialized nor stiffened the vocal process to resist lateralizing forces. We conclude that medialization laryngoplasty provides bulk and support for defects of the membranous region of the vocal fold, but does not appear to close a posterior glottal gap. The selection of a surgical procedure to treat glottal incompetence should take into account the unique biomechanical properties of the anterior (membranous vocal folds) and posterior (cartilaginous portion) glottis.