Internal Angle Research Articles

Relationship between kinesiophobia, isometric hip and knee torques to pelvic, hip and knee motion during the single-leg drop jump in women with patellofemoral pain: A cross-sectional study

BackgroundIndividuals with patellofemoral pain (PFP) have kinesiophobia and hip and knee strength deficits. These factors may be related to kinematic alterations of pelvic, hip and knee during a more demanding functional activity, such as jumping landing. The aim was to investigate the relationships between kinesiophobia and hip/knee torque to pelvic/hip/knee kinematics during the single-leg drop vertical jump in women with PFP. MethodThirty women with PFP were assessed with Tampa Scale for Kinesiophobia; isokinetic dynamometry of the hip extensor, hip abductor, and knee extensor; and three-dimensional motion analysis system during the single-leg drop vertical jump. A Pearson correlation matrix was used to investigate relationship among variables. ResultsFair correlations were found between increased kinesiophobia and increased peak hip internal rotation angle (r = 0.43; p = 0.018) as well as between greater peak knee extensor torque and greater peak knee flexion (r = 0.41; p = 0.022). Moderate to good correlation was found between increased peak hip abductor torque and increased peak contralateral pelvic drop (r = 0.52; p = 0.003). No other significant correlations were found between variables. ConclusionsKinesiophobia is associated with hip kinematics, but not with knee kinematics, during the single-leg vertical drop jump in women with PFP. The greater hip abductor torque is associated with greater contralateral pelvic drop. The positive relationship between knee extensor torque and knee flexion indicates that rehabilitation programs involving quadriceps muscle strengthening may assist women with PFP in control knee flexion and improve load absorption during jumping landing.

Macro-micro mechanical study of principal stress rotation in granular materials using DEM simulations of hollow cylinder test

The dependency of sand behavior anisotropy on microstructure reveals the importance of macro-micro mechanical analysis of the principal stresses rotation effect on the strength-deformation response of granular material. In this study multi-scale analysis of the granular material's behavior using three-dimensional discrete element method simulations of the hollow cylinder test was presented. The effect of principal stresses rotation (α) on the macro-mechanical behavior of the soil was investigated from the micro-mechanical anisotropy aspect. It was observed that principal stress rotation affects the anisotropy coefficient and directional distribution of all micro-parameters which can change the soil's behavior according to loading conditions. The stress-force-fabric relationship was used to analyze the microstructure's stress state based on micro-parameters anisotropy coefficients. In addition to the good agreement between stress-force-fabric and general stress tensors, the decreasing trend of the maximum deviator stress and internal friction coefficient angle with increasing α can be observed for both stress tensors.

A BF2 Chelate Exhibiting Excimer-like Fluorescence with an Unusually Large Stokes Shift in the Crystalline Phase.

The target mono-BF2 complex is weakly emissive in fluid solution because radiationless decay of the excited-singlet state is promoted through an intramolecular N⋅⋅⋅H-N hydrogen bond. The lack of mirror symmetry for this compound is attributed to vibronic effects, as reported previously for the bis-BF2 complex (BOPHY). Red-shifted fluorescence is observed from single crystals, the emission quantum yield approaching 30 % with a fluorescence lifetime of 2 ns. The large Stokes shift of 5,700 cm-1 helps minimize self-absorption. Crystallography indicates that the internal fold and twist angles are increased substantially in the crystal, but the hydrogen bond is weakened relative to solution. The crystal structure is compiled from pairs of head-to-tail molecules having a shift of ca. 4.1 Å and closest approach of ca. 3.5 Å. These molecular pairs are arranged in columns, which, in turn, assemble into sheets. The proximity favors excitonic coupling between individual molecules, with the coupling strength obtained by analysis of the absorption spectrum reaching ca. 1,000 cm-1 . Both the ideal dipole approximation and the extended dipole methodology seriously overestimate the coupling strength, but the atomic transition charge density procedure leads to good agreement with experiment. Emission is attributed to the closely coupled molecular pair functioning in an excimer-like manner with the exciton trapped in a local minimum. Increasing temperature causes a slight blue shift and loss of fluorescence.

The Relationship Between the Effects of Lateral Wedge Insoles and Kinematic Chain Dynamics Between the Hindfoot and Lower Leg in Patients With Osteoarthritis of the Knee.

Purpose We aim to determine whether kinematic chain dynamics of the hindfoot and lower leg are involved in the effect of a lateral wedge insole (LWI) on reducing lateral thrust among patients with medial compartment knee osteoarthritis (KOA). Participants and methods Eight patients with knee osteoarthritis were included in the study. Evaluation of the kinematic chain and gait analysis was performed using an inertial measurement unit (IMU). The dynamics of the kinematic chain were calculated as linear regression coefficients of the external rotation angle of the lower leg relative to the inversion angle of the hindfoot during repeated inversion and eversion of the foot in the standing position (kinematic chain ratio (KCR)). Walk tests were performed under four conditions: barefoot (BF), neutral insole (NI) with an incline of 0 degrees, and LWI with an incline of approximately 5 and 10 degrees (5LWI and 10LWI, respectively). Results The mean (± standard deviation (SD)) KCR was 1.4 ± 0.5. The KCR was significantly correlated with the change in 5LWI lateral thrust acceleration relative to BF (r = 0.74). A significant correlation was also observed between changes in the hindfoot evolution angle and lower leg internal rotation angle with a 10LWI with respect to BF and NI, and changes in lateral thrust acceleration. Conclusion The results of this study suggest that the kinematic chain is involved in the effects of an LWI in patients with knee osteoarthritis.

Shear stress metrics associated with pro-atherogenic high-risk anatomical features in a carotid artery bifurcation model

BackgroundDiseases associated with atherosclerotic plaques in the carotid artery are a major cause of deaths in the United States. Blood-flow-induced shear-stresses are known to trigger plaque formation. Prior literature suggests that the internal carotid artery sinus is prone to atherosclerosis, but there is limited understanding of why only certain patients are predisposed towards plaque formation. MethodsWe computationally investigate the effect of vessel geometry on wall-shear-stress distribution by comparing flowfields and wall-shear-stress-metrics between a low-risk and a novel predisposed high-risk carotid artery bifurcation anatomy. Both models were developed based on clinical risk estimations and patient-averaged anatomical features. The high-risk geometry has a larger internal carotid artery branching angle and a lower internal-to-carotid-artery-diameter-ratio. A patient-averaged physiological carotid artery inflow waveform is used. FindingsThe high-risk geometry experiences stronger flow separation in the sinus. Furthermore, it experiences a more equal flow split at the bifurcation, thereby reducing internal carotid artery flowrate and increasing atherosclerosis-prone low-velocity areas. Lowest time-averaged-wall-shear-stresses are present at the sinus outer wall, where plaques are often found, for both geometries. The high-risk geometry has significantly high, unfavorable oscillatory-shear-index values not found in the low-risk geometry. High oscillatory-shear-index areas are located at the vessels outside walls distal to the bifurcation and on the sinus wall. InterpretationThese results highlight the effectiveness of oscillatory-shear-index, to augment classical time-averaged-wall-shear-stress, in evaluating pro-atherogenic geometry features. Furthermore, the flow split at the bifurcation is a promising clinical indicator for atherosclerosis risk as it can be directly accessed using clinical imaging, whereas shear-stress-metrics cannot.

Hip Pain after Distal Femoral Derotational Osteotomy for a Patient with Patellar Instability: A Case Report

Increased torsional deformity of femur is one of the most important factors in recurrent patellofemoral instability. And distal femoral derotational osteotomy is an effective treatment option in patients with increased femoral torsional deformity. However, groin pain is a rare complication after femoral derotational osteotomy. The patient was a 23-year-old female suffering from anterior knee pain and patellar instability in her left leg. Continuous CT scans of the hip, knee, and ankle were performed and the femoral anteversion was 44.99°. Considering the significant enlargement of the femoral internal torsion which may contribute most for dislocation of patella, we did a derotational osteotomy of distal femur. The anterior knee pain and patellar instability were resolved after surgery. The femoral internal torsion angle was corrected to 21.47°. But she developed left hip pain in the groin area which she had never encountered before 1 year after the surgery. We believed that the hip pain was closely related to the surgery. And the imaging and follow-up partly confirmed this. The situation of the hip joint should be carefully evaluated before doing derotational osteotomy in recurrent patellofemoral instability and patient should be informed that derotational osteotomy may cause hip pain. Clinical studies are needed to further clarify the impact of derotational osteotomy on the hip.

Universities’ and Academics’ Resources Shaping Satisfaction and Engagement: An Empirical Investigation of the Higher Education System

Higher education research has claimed that the successful future of the educational service is highly dependent on the competencies and observations of the participants in the system, where service quality, employee satisfaction and engagement play an essential role in organizational competitiveness. Therefore, to contribute to the scarce investigation of the role of the institutions’ efforts in the support of engaged academics, we aim to assess the quality of higher education from an internal angle by investigating universities’ and academics’ resources as the antecedents of job satisfaction and engagement. The data from a survey with 322 academics from Macedonian public universities were analyzed using partial least squares structural equations modelling. The results of the estimated model reveal that institutional and educational capacities and academics’ adequate competencies are essential for accomplishing favorable perceptions, leading to a committed community dedicated to improving the higher education system. The implications underline that it is vital to recognize the institution’s potential by identifying and assessing the resources and capacities it possesses or can access. Moreover, to involve satisfied employees, universities must encourage academics’ position and integrity in the institution and promote harmonious collaboration while motivating their capacities and excellence development.

The effect of auxeticity on the vibration of conical sandwich shells with ring support under various boundary conditions

Auxetic materials, materials demonstrating negative Poisson's ratio, have revolutionized the use of materials in industries, as they demonstrate superb acoustic response, fracture resistance, and energy absorption. For the first time, this study embraces the free vibration of conical shells consisting of an auxetic core with and without ring support under various boundary conditions. First, the material characteristics of the auxetic core are calculated by means of a micromechanical approach. Afterwards, the kinematic motion equations of the conical shell are derived utilizing the first-order shear deformation theory. Finally, the governing equations are solved using the powerful generalized differential quadrature element method (GDQEM). The primary goal of this paper is to study the role of implementing an auxetic core as well as ring support in determining the vibrational behavior of the structure. The results of the study showed that the honeycomb interior angle and the presence of ring support can significantly affect the natural frequency of the structure. Lower frequencies can be reached as the interior angle increases. The importance of ring position is found to be highly dependent on the longitudinal mode shapes of vibration. The impact of ring position on natural frequencies is affected by the semi-vertex angle of the cone, and a shift in frequency peaks can be observed by increasing the semi-vertex angle.

Discharge Coefficient of Symmetrical Stepped and Triangular Labyrinth Side Weirs in a Subcritical Flow Regime

The labyrinth side weir structure is an optimal solution to regulate and divert excess flows across rivers, and irrigation and drainage channels when the opening length of the side weir is limited. Changing the geometry of the side weir is considered one way to improve its efficiency. The present study investigates the hydraulic effects of stepped labyrinth side weirs to increase their discharge capacity. To estimate the outflow over symmetrical stepped labyrinth side weir, the discharge coefficient needs to be determined. Normal triangular labyrinth side weir in one cycle mode has been modified by increasing the crest path using different steps. A total of 417 experiments were conducted on normal and stepped side weirs for various weir opening lengths, weir heights, internal head angles, and hydraulic conditions. The results were analyzed and compared. It was found that efficiency improved, and the discharge coefficient increased as the number of the steps decreased. Furthermore, the water surface profile becomes more uniform with decreasing number of steps. A lower number of steps, smaller head angle, and high weir length produce a higher discharge coefficient by approximately 15%–35% compared to a normal triangular labyrinth side weir; in addition, the Knope length decreases by approximately 40%–70% for the same effective length. Additionally, a reliable equation to estimate the discharge coefficient of the stepped labyrinth side weir was presented. The results of this study can be used to design side weirs with high hydraulic performance when the weir-included angle selected is small or there is a lack of space.

Relationship between the knee valgus moment and the hip abductor and adductor activity during single-leg landing

ObjectivesTo reveal the relationship between the knee valgus moment (KVM) and the hip abductor and adductor activity during single-leg landing. DesignA cross-sectional study. SettingLaboratory-based, between April 2020 and May 2021. ParticipantsThirty female collegiate athletes. Main outcome measuresKVM, hip adduction angle, hip internal rotation angle, knee valgus angle (KVA), gluteus medius muscle activity, adductor longus muscle activity, adductor longus to gluteus medius activity ratio (ADD/GMED), and vertical component of the ground reaction force (vGRF). ResultsStepwise multiple regression analysis was performed. KVM was significantly positively associated with KVA (β = 0.613, p < 0.001), vGRF (β = 0.367, p = 0.010), and ADD/GMED (β = 0.289, p = 0.038). ConclusionsIncreased KVA, vGRF, and ADD/GMED were the independent factors that contributed to increased KVM during single-leg landing, and only ADD/GMED was found among the muscle activity values. The relative muscle activity of the gluteus medius and adductor longus, rather than those of the gluteus medius or adductor longus alone, may be useful in preventing anterior cruciate ligament injury during single-leg landing.

Quantitative Analysis of Deformity in Digital Model of Congenital Radioulnar Synostosis

The deformity of congenital radioulnar synostosis is quite complicated and difficult. This study aims to find out the related factors of the "forearm rotation angle" (FR) which relate to the severity of congenital radioulnar synostosis (CRUS), and try to quantify the internal relations of each deformity and help to understand the reconstruction method in surgery treatment of this disease. This study is case series research. We established 48 digital three-dimensional forearm bone models of 48 patients with congenital radioulnar synostosis classified as Cleary and Omer type 3. All the patients were treated at our institution from January 2010 to June 2016. In total, 10 independent deformities (the rotation angle of forearm; the internal rotation, radial, and dorsal angulation of radius and ulna; the relative length of osseous fusion at PRUJ; the relative dislocation distance of distal radioulnar joint; the relative area of proximal radial epiphysis) involved in the CRUS complex deformity were measured. Pearson correlation analysis for each deformity which was mentioned above was performed, and multivariate linear regression analysis was also performed with FR as the dependent variable and the other deformities as the influential factors. The "dorsal angle of radius" (DAR, 21.69° ± 21.55°) had the strongest correlation with the FR (79.72° ± 40.39°), the Pearson correlation coefficient was 0.601 (p < 0.01), the internal rotation angle of the radius (IRAR, 82.69° ± 54.98°) had a moderate correlation with FR, the Pearson correlation coefficient was 0.552 (p < 0.01). A forearm deformity equation was established: FR=35.896 + 0.271 DAR + 0.989 IRAR. The dorsal angulation deformity of radius may be the most important deformity that effects the severity of CRUS and should be correct in the first place during reconstruction operation.

Determination of optimal padeye position of modified suction caissons in the sand under monotonic inclined loading

Modified suction caissons (MSCs) acting as floating platform foundations will be subjected to inclined loading induced by wind waves and currents, thus, it is of significance to investigate its inclined bearing capacity. Model tests and numerical simulations were conducted on the MSCs embedded in the sand to study the monotonic inclined bearing behavior. Test results show that the inclined capacity firstly increases, and then, decreases as the padeye position moves downward along the caisson wall. The optimum padeye position corresponding to maximum inclined bearing capacity locates at the 0.5 times the internal compartment length below the lid when the loading angle equals 20°. The contribution of passive suction to the capacity may be ignorable when the loading angle is relatively small, and the passive earth pressure is predominant. It was also found that the increase of the external structure length can improve the inclined bearing capacity compared with the increase of external structure width. The relationship between the ultimate bearing capacity and the padeye position follows a Gaussian function. Considering the external structure dimensions, loading angle, and padeye position, a normalized formula is proposed to determine the ultimate bearing capacity. Finally, the optimal padeye position will be found for the floating platform.

Excitation of second harmonic terahertz surface magnetoplasmons over a rippled surface of n-InSb

We analyzed the excitation of second harmonic (SH) terahertz (THz) surface magnetoplasmons (SMPs) over a n-type semiconductor (n-InSb)-free space interface. P-polarized laser obliquely incidents on the magnetized rippled surface of semiconductor with frequency ω and wave number k0z and k0x and exerts a ponderomotive force on free electrons of semiconductor surface and imparts second harmonic oscillatory velocity v→2ω. Second harmonic oscillatory velocity v→2ω couples with modulated electron density nq of rippled surface to produce a second harmonic nonlinear current J→2ωnl, which resonantly derives SH THz SMPs with wave number k2z=2k0z+q and frequency 2ω. SH THz SMPs amplitude increases with applied external magnetic field as well as with incident angle and gets the maximum value then decreases further increase in the applied external magnetic field and incident angle. The conversion efficiency of SH THz SMPs amplitude is achieved up to 4.2%.

Experimental and numerical simulation on the sliding process of roof rock blocks triggered by dynamic disturbance

With the excavation of underground opening, the roof rock block may fall under external dynamic disturbance. In this paper, the roof rock mass was simplified as a rock block system composed of trapezoidal rock blocks. A series of experiments and numerical simulations were performed to study the sliding process of the key block under the horizontal static clamping load and vertical impact disturbance. The propagation of stress wave in the block system were captured and analyzed by using high-speed camera and digital image correlation technique. The results reveal that a pendulum-type wave was generated due to the propagation and superposition of stress waves in the block system. Therefore, the governing mechanism of the sliding displacement of the key block was clarified based on the propagation of incident stress waves or pendulum-type waves. Meanwhile, it is found that the sliding distance of the key block decreases in a power function with the increasing friction coefficient, or decreases in a parabolic function with the increasing trapezoid internal angle. Finally, a case study on the roof block sliding of the roadway at a gold mine was conducted, and it is concluded that the sliding of the key block resulted from the coupled effects of “shear driving” and “low friction” driven by stress wave propagation, regardless of a single or multi-layer rock block system. These results may provide technical guideline for preventing rock-falling accidents caused by blasting disturbances in underground mining.

The effect of femoral component valgus/varus angle on the mid-term efficacy of unicondylar knee arthroplasty

ABSTRACT Objective: To investigate the effect of femoral component valgus/varus angle (FCVA) on the mid-term outcome after unicondylar knee arthroplasty. Methods: Patients who underwent unicompartmental knee replacement in the Department of Bone and Joint Surgery, were retrospectively analyzed. According to the postoperative femoral prosthesis internal and external rotation angle, patients were divided into six groups the postoperative femoral prosthesis internal and external rotation angle: standard group, mildly abnormal group. The patients were followed up for 12 months, and complications were recorded during the follow-up period. The Range of motion (ROM), visual analog scale (VAS), and Knee society score (KSS) were compared between the six groups. Results: One hundred twenty-four patients with 124 knees were included in this study. There were no statistical differences in age, gender, body mass index, preoperative ROM, or preoperative VAS, KSS-C, and KSS-F scores among the six groups. Comparison of postoperative outcomes and efficacy grades showed that: (1) the differences in ROM grades, as well as VAS, KSS-C, and KSS-F efficacy at 12 months postoperatively were statistically significant in all six groups by rank sum test; and patients in the normal group had better ROM grades and KSS-F grades than those in the mild and severe abnormality groups; (2) During the follow-up, no patient records had other serious complications such as periprosthetic infection, prosthetic loosening, periprosthetic fracture, and spacer dislocation. Conclusion: Controlling the femoral prosthetic internal rotation angle between 6° and 0° in unicompartmental knee replacements can lead to better mid-term outcomes for patients.

Optimum frequency response with decentralized drivers in power system

AbstractThis document presents a novel methodology to optimize the power system frequency response based on the implementation of decentralized controllers. The proposed method focuses on the control of the internal rotor angle in the selected generator, which allows its governor to act as a decentralized controller that requires as input local measurements. Through a proposed optimization process, it is first possible to establish a set of optimal parameters for each controller and, second, to determine the required phasor measurement units (PMUs) and their locations that are necessary to be installed in a power system. This comprehensive proposal is based on the time domain evaluation of the frequency response when multiple scenarios of deviations between demand and generation occur. Finally, the new proposal is applied to the IEEE 39‐bus test system to validate its advantages; for this, the test power system as well as the proposed controllers are implemented in DIgSILENT PowerFactory, along with Python to manage the optimization process.

Effect of spatial arrangement and clinical service lifetime simulation on the retention of magnetic units used in implant-anchored orbital prostheses

Statement of problemEvidence for the optimal spatial arrangement of magnetic attachments in implant-supported orbital prostheses is lacking. PurposeThe purpose of this in vitro study was to assess the effect of 6 different spatial arrangements on the retentive force of magnetic attachments following the in vitro simulation of clinical service by insertion-removal test cycles and the contribution of artificial aging to the morphological alterations induced on the magnetic surfaces. Material and methodsNi-Cu-Ni plated disk-shaped neodymium (Nd) magnetic units (d=5 mm, h=1.6 mm) were secured on leveled (50×50×5 mm, n=3) and angled (40×45×40 mm, interior angle=90 degrees, n=3) pairs of test panels in 6 different spatial arrangements: triangular_leveled (TL), triangular_angled (TA), square_leveled (SL), square_angled (SA), circular_leveled (CL), and circular_angled (CA) generating corresponding test assemblies (N=6). TL and TA arrangements included 3 magnetic units (3-magnet groups) and SL, SA, CL, and CA 4 (4-magnet groups). The retentive force (N) was measured at a mean crosshead speed of 10 mm/min (n=10). Each test assembly was subjected to insertion-removal test cycles with a 9-mm amplitude, ν=0.1 Hz, and n=10 consequent retentive force measurements at a crosshead speed of 10 mm/min at 540, 1080, 1620, and 2160 test cycles. Surface roughness alterations following the 2160 test cycles were measured by calculating the Sa, Sz, Sq, Sdr, Sc, and Sv parameters with an optical interferometric profiler with 5 new magnetic units used as a control group. Data were analyzed with 1-way ANOVA and Tukey HSD post hoc tests (α=.05). ResultsThe 4-magnet groups had statistically significantly higher retentive force than the 3-magnet ones at baseline and following the 2160 test cycles (P<.05). In the 4-magnet group, the ranking at baseline was SA<CA<CL<SL (P<.05) and following the test cycles SA=CA<CL<SL (P<.05). No statistically significant differences were found in the surface roughness parameters (Sa, Sz, Sq, Sdr, Sc, and Sv) following the 2160 test cycles among the experimental groups tested (P>.05). ConclusionsFour magnetic attachments placed on an SL spatial arrangement resulted in the highest retention force but presented with the highest force reduction following the in vitro simulation of clinical service by insertion-removal test cycles.

The Association of Trunk and Hip Kinematic With Knee Abduction Angle During Single-Leg Landing

Objectives: Children aged 10 to 12 years often show dangerous maneuvers during landing, which include increased knee valgus, placing them at higher risk of anterior cruciate ligament (ACL) injuries. The study aimed to investigate the relation of the trunk and hip kinematics with the peak knee abduction angle during single-leg landing among preadolescent female soccer players. Methods: Thirty-six preadolescent female soccer players aged 10 to 12 years attended the study. Participants did a static trial and after that performed landing trials. A single-leg landing was applied to assess the landing kinematics. A three-dimensional motion capture system was applied to analyze trunk, hip, and knee kinematics. Results: Pearson correlation coefficient demonstrated a significantly positive relationship between peak hip internal rotation angle (r=0.361) (P=0.03) and peak knee abduction angle. Furthermore, no significant relationship was identified between peak hip adduction (r=-0.102) (P=0.55), peak trunk rotation (r=0.239) (P=0.16), peak trunk lateral flexion (r=0.052) (P=0.76), and peak valgus knee. Discussion: Peak hip rotation angle was correlated with the valgus knee with a weak correlation value among preadolescent female soccer players. Future studies should consider kinematic risk factors related to ACL injuries in combination with neuromuscular control trunk and hip during more demanding tasks.

High-Quality AlN Grown on Si(111) Substrate by Epitaxial Lateral Overgrowth

We report on the epitaxial lateral overgrowth (ELO) of high-quality AlN on stripe-patterned Si(111) substrates with various trench widths. By narrowing down the trench and ridge widths of patterned Si substrates, crack-free, 6-micrometer-thick, high-quality AlN films on Si substrates were produced. The full-width-at-half-maximum values of the X-ray-diffraction rocking curves for the AlN (0002) and (101¯2) planes were as low as 260 and 374 arcsec, respectively, corresponding to a record low dislocation density of 1.3 × 109 cm−2. Through the combination of a micro-Raman study and the X-ray diffraction analysis, it was found that narrowing the stripe width from 5 μm to 3 μm can reduce the vertical growth thickness before coalescence, resulting in a large decrease in the internal tensile stress and tilt angle, and, therefore, better suppression in the cracks and dislocations of the ELO–AlN. This work paves the way for the fabrication of high-performance Al(Ga)N-based thin-film devices such as ultraviolet light-emitting diodes and AlN bulk acoustic resonators grown on Si.

Asymmetric rotations and dimerization driven by normal to modulated phase transition in 4-biphenylcarboxy coupled L-phenylalaninate.

Amongst the derivatives of 4-biphenylcarboxylic acid and amino acid esters, the crystal structure of 4-biphenylcarboxy-(L)-phenylalaninate is unusual owing to its monoclinic symmetry within a pseudo-orthorhombic crystal system. The distortion is described by a disparate rotational property around the chiral centers (ϕchiral ≃ -129° and 58°) of the two molecules in the asymmetric unit. Each of these molecules comprises planar biphenyl moieties (ϕbiphenyl = 0°). Using temperature-dependent single-crystal X-ray diffraction experiments we show that the compound undergoes a phase transition below T ∼ 124 K that is characterized by a commensurate modulation wavevector, q = δ(101), δ = ½. The (3+1)-dimensional modulated structure at T = 100 K suggests that the phase transition drives the biphenyl moieties towards noncoplanar conformations with significant variation of internal torsion angle (ϕmaxbiphenyl ≤ 20°). These intramolecular rotations lead to dimerization of the molecular stacks that are described predominantly by distortions in intermolecular tilts (θmax ≤ 20°) and small variations in intermolecular distances (Δdmax ≃ 0.05 Å) between biphenyl molecules. Atypical of modulated structures and superstructures of biphenyl and other polyphenyls, the rotations of individual molecules are asymmetric (Δϕbiphenyl ≈ 5°) while ϕbiphenyl of one independent molecule is two to four times larger than the other. Crystal-chemical analysis and phase relations in superspace suggest multiple competing factors involving intramolecular steric factors, intermolecular H-C...C-H contacts and weak C-H...O hydrogen bonds that govern the distinctively unequal torsional properties of the molecules.