Precrystallization solute assemblies and crystal symmetry.

Solution crystallization is a part of the synthesis of materials ranging from geological and biological minerals to pharmaceuticals, fine chemicals, and advanced electronic components. Attempts to predict the structure, growth rates and properties of emerging crystals have been frustrated, in part, by the poor understanding of the correlations between the oligomeric state of the solute, the growth unit, and the crystal symmetry. To explore how a solute monomer or oligomer is selected as the unit that incorporates into kinks and how crystal symmetry impacts this selection, we combine scanning probe microscopy, optical spectroscopy, and all-atom molecular simulations using as examples two organic materials, olanzapine (OZPN) and etioporphyrin I (EtpI). The dominance of dimeric structures in OZPN crystals has spurred speculation that the dimers preform in the solution, where they capture the majority of the solute, and then assemble into crystals. By contrast, EtpI in crystals aligns in parallel stacks of flat EtpI monomers unrelated by point symmetry. Raman and absorption spectroscopies show that solute monomers are the majority solute species in solutions of both compounds. Surprisingly, the kinetics of incorporation of OZPN into kinks is bimolecular, indicating that the growth unit is a solute dimer, a minority solution component. The disconnection between the dominant solute species, the growth unit, and the crystal symmetry is even stronger with EtpI, for which the (010) face grows by incorporating monomers, whereas the growth unit of the (001) face is a dimer. Collectively, the crystallization kinetics results with OZPN and EtpI establish that the structures of the dominant solute species and of the incorporating solute complex do not correlate with the symmetry of the crystal lattice. In a broader context, these findings illuminate the immense complexity of crystallization scenarios that need to be explored on the road to the understanding and control of crystallization.

Prediction of Mefenamic Acid Crystal Shape by Random Forest Classification.

OBJECTIVE: Particle shape can have a significant impact on the bulk properties of materials. This study describes the development and application of machine-learning models to predict the crystal shape of mefenamic acid recrystallized from organic solvents. METHODS: Crystals were grown in 30 different solvents to establish a dataset comprising solvent molecular descriptors, process conditions and crystal shape. Random forest classification models were trained on this data and assessed for prediction accuracy. RESULTS: The highest prediction accuracy of crystal shape was 93.5% assessed by fourfold cross-validation. When solvents were sequentially excluded from the training data, 32 out of 84 models predicted the shape of mefenamic acid crystals for the excluded solvent with 100% accuracy and a further 21 models had prediction accuracies from 50-100%. Reducing the feature set to only solvent physical property descriptors and supersaturations resulted in higher overall prediction accuracies than the models trained using all available or another selected subset of molecular descriptors. For the 8 solvents on which the models performed poorly (< 50% accuracy), further characterisation of crystals grown in these solvents resulted in the discovery of a new mefenamic acid solvate whereas all other crystals were the previously known form I. CONCLUSIONS: Random forest classification models using solvent physical property descriptors can reliably predict crystal morphologies for mefenamic acid crystals grown in 20 out of the 28 solvents included in this work. Poor prediction accuracies for the remaining 8 solvents indicate that further factors will be required in the feature set to provide a more generalized predictive morphology model.

Recent Advances in Co-processed APIs and Proposals for Enabling Commercialization of These Transformative Technologies.

Optimized physical properties (e.g., bulk, surface/interfacial, and mechanical properties) of active pharmaceutical ingredients (APIs) are key to the successful integration of drug substance and drug product manufacturing, robust drug product manufacturing operations, and ultimately to attaining consistent drug product critical quality attributes. However, an appreciable number of APIs have physical properties that cannot be managed via routes such as form selection, adjustments to the crystallization process parameters, or milling. Approaches to control physical properties in innovative ways offer the possibility of providing additional and unique opportunities to control API physical properties for both batch and continuous drug product manufacturing, ultimately resulting in simplified and more robust pharmaceutical manufacturing processes. Specifically, diverse opportunities to significantly enhance API physical properties are created if allowances are made for generating co-processed APIs by introducing nonactive components (e.g., excipients, additives, carriers) during drug substance manufacturing. The addition of a nonactive coformer during drug substance manufacturing is currently an accepted approach for cocrystals, and it would be beneficial if a similar allowance could be made for other nonactive components with the ability to modify the physical properties of the API. In many cases, co-processed APIs could enable continuous direct compression for small molecules, and longer term, this approach could be leveraged to simplify continuous end-to-end drug substance to drug product manufacturing processes for both small and large molecules. As with any novel technology, the regulatory expectations for co-processed APIs are not yet clearly defined, and this creates challenges for commercial implementation of these technologies by the pharmaceutical industry. The intent of this paper is to highlight the opportunities and growing interest in realizing the benefits of co-processed APIs, exemplified by a body of academic research and industrial examples. This work will highlight reasons why co-processed APIs would best be considered as drug substances from a regulatory perspective and emphasize the areas where regulatory strategies need to be established to allow for commercialization of innovative approaches in this area.

Peptide Isolation via Spray Drying: Particle Formation, Process Design and Implementation for the Production of Spray Dried Glucagon.

PURPOSE: Spray drying plays an important role in the pharmaceutical industry for product development of sensitive bio-pharmaceutical formulations. Process design, implementation and optimisation require in-depth knowledge of process-product interactions. Here, an integrated approach for the rapid, early-stage spray drying process development of trehalose and glucagon on lab-scale is presented. METHODS: Single droplet drying experiments were used to investigate the particle formation process. Process implementation was supported using in-line process analytical technology within a data acquisition framework recording temperature, humidity, pressure and feed rate. During process implementation, off-line product characterisation provided additional information on key product properties related to residual moisture, solid state structure, particle size/morphology and peptide fibrillation/degradation. RESULTS: A psychrometric process model allowed the identification of feasible operating conditions for spray drying trehalose, achieving high yields of up to 84.67%, and significantly reduced levels of residual moisture and particle agglomeration compared to product obtained during non-optimal drying. The process was further translated to produce powders of glucagon and glucagon-trehalose formulations with yields of >83.24%. Extensive peptide aggregation or degradation was not observed. CONCLUSIONS: The presented data-driven process development concept can be applied to address future isolation problems on lab-scale and facilitate a systematic implementation of spray drying for the manufacturing of sensitive bio-pharmaceutical formulations.

Use of Terahertz-Raman Spectroscopy to Determine Solubility of the Crystalline Active Pharmaceutical Ingredient in Polymeric Matrices during Hot Melt Extrusion.

Polymer-based amorphous solid dispersions (ASDs) comprise one of the most promising formulation strategies devised to improve the oral bioavailability of poorly water-soluble drugs. Exploitation of such systems in marketed products has been limited because of poor understanding of physical stability. The internal disordered structure and increased free energy provide a thermodynamic driving force for phase separation and recrystallization, which can compromise therapeutic efficacy and limit product shelf life. A primary concern in the development of stable ASDs is the solubility of the drug in the polymeric carrier, but there is a scarcity of reliable analytical techniques for its determination. In this work, terahertz (THz) Raman spectroscopy was introduced as a novel empirical approach to determine the saturated solubility of crystalline active pharmaceutical ingredient (API) in polymeric matrices directly during hot melt extrusion. The solubility of a model compound, paracetamol, in two polymer systems, Affinisol 15LV (HPMC) and Plasdone S630 (copovidone), was determined by monitoring the API structural phase transitions from crystalline to amorphous as an excess of crystalline drug dissolved in the polymeric matrix. THz-Raman results enabled construction of solubility phase diagrams and highlighted significant differences in the solubilization capacity of the two polymer systems. The maximum stable API-load was 20 wt % for Affinisol 15LV and 40 wt % for Plasdone S630. Differential scanning calorimetry and XRPD studies corroborated these results. This approach has demonstrated a novel capability to provide real-time API-polymer phase equilibria data in a manufacturing relevant environment and promising potential to predict solid-state solubility and physical stability of ASDs.

Combined Chemoinformatics Approach to Solvent Library Design Using clusterSim and Multidimensional Scaling.

Reported here is a rational approach for the selection of solvents intended for use in physical form screening based on a novel chemoinformatics analysis of solvent properties. A comprehensive assessment of eight clustering methods was carried out on a series of 94 solvents described by calculated molecular descriptors using the clusterSim package in R. The effectiveness of clustering methods was evaluated using a range of statistical measures as well as increasing efficiency of solid form discovery using a cluster-based solvent selection approach. Multidimensional scaling was used to illustrate cluster analysis on a two-dimensional solvent map. The map presented here is a valuable tool to aid efficient solvent selection in physical form screens. This tool is equally applicable to any scientific area which requires a solubility dependent decision on solvent choice.

Comparative Study on Adaptive Bayesian Optimization for Batch Cooling Crystallization for Slow and Fast Kinetic Regimes.

Crystallization kinetic parameter estimation is important for the classification, design, and scale-up of pharmaceutical manufacturing processes. This study investigates the impact of supersaturation and temperature on the induction time, nucleation rate, and growth rate for the compounds lamivudine (slow kinetics) and aspirin (fast kinetics). Adaptive Bayesian optimization (AdBO) has been used to predict experimental conditions that achieve target crystallization kinetic values for each of these parameters of interest. The use of AdBO to guide the choice of the experimental conditions reduced material usage up to 5-fold when compared to a more traditional statistical design of experiments (DoE) approach. The reduction in material usage demonstrates the potential of AdBO to accelerate process development as well as contribute to Net-Zero and green chemistry strategies. Implementation of AdBO can lead to reduced experimental effort and increase efficiency in pharmaceutical crystallization process development. The integration of AdBO into the experimental development workflows for crystallization development and kinetic experiments offers a promising avenue for advancing the field of autonomous data collection exploiting digital technologies and the development of sustainable chemical processes.

A complementary experimental and computational study of loxapine succinate and its monohydrate.

The crystal structures of loxapine succinate [systematic name: 4-(2-chlorodibenzo[b,f][1,4]oxazepin-11-yl)-1-methylpiperazin-1-ium 3-carboxypropanoate], C18H19ClN3O(+)·C4H5O4(-), and loxapine succinate monohydrate {systematic name: bis[4-(2-chlorodibenzo[b,f][1,4]oxazepin-11-yl)-1-methylpiperazin-1-ium] succinate succinic acid dihydrate}, 2C18H19ClN3O(+)·C4H4O4(2-)·C4H6O4·2H2O, have been determined using X-ray powder diffraction and single-crystal X-ray diffraction, respectively. Fixed cell geometry optimization calculations using density functional theory confirmed that the global optimum powder diffraction derived structure also matches an energy minimum structure. The energy calculations proved to be an effective tool in locating the positions of the H atoms reliably and verifying the salt configuration of the structure determined from powder data. Crystal packing analysis of these structures revealed that the loxapine succinate structure is based on chains of protonated loxapine molecules while the monohydrate contains dispersion stabilized centrosymmetric dimers. Incorporation of water molecules within the crystal lattice significantly alters the molecular packing and protonation state of the succinic acid.

2-Methyl-4-(4-methyl-piperazin-1-yl)-10H-thieno[2,3-b][1,5]benzodiazepine (olanzapine) propan-2-ol disolvate.

In the title solvate, C17H20N4S·2C3H8O, pairs of olanzapine mol-ecules related by a centre of inversion stack along the a axis, forming columns, which are packed parallel to each other along the b axis, forming a sheet arrangement. The columns within these sheets are hydrogen bonded to each other through the propan-2-ol solvent mol-ecules. The diazepine ring of the olanzapine exists in a puckered conformation with the thiophene and phenyl rings making a dihedral angle of 57.66 (7)° and the piperazine ring adopts a chair conformation with the methyl group in an equatorial position.

Machine Learning-Derived Correlations for Scale-Up and Technology Transfer of Primary Nucleation Kinetics.

Scaling up and technology transfer of crystallization processes have been and continue to be a challenge. This is often due to the stochastic nature of primary nucleation, various scale dependencies of nucleation mechanisms, and the multitude of scale-up approaches. To better understand these dependencies, a series of isothermal induction time studies were performed across a range of vessel volumes, impeller types, and impeller speeds. From these measurements, the nucleation rate and growth time were estimated as parameters of an induction time distribution model. Then using machine learning techniques, correlations between the vessel hydrodynamic features, calculated from computational flow dynamic simulations, and nucleation kinetic parameters were analyzed. Of the 18 machine learning models trained, two models for the nucleation rate were found to have the best performance (in terms of % of predictions within experimental variance): a nonlinear random Forest model and a nonlinear gradient boosting model. For growth time, a nonlinear gradient boosting model was found to outperform the other models tested. These models were then ensembled to directly predict the probability of nucleation, at a given time, solely from hydrodynamic features with an overall root mean square error of 0.16. This work shows how machine learning approaches can be used to analyze limited datasets of induction times to provide insights into what hydrodynamic parameters should be considered in the scale-up of an unseeded crystallization process.

Tautomerism unveils a self-inhibition mechanism of crystallization.

Modifiers are commonly used in natural, biological, and synthetic crystallization to tailor the growth of diverse materials. Here, we identify tautomers as a new class of modifiers where the dynamic interconversion between solute and its corresponding tautomer(s) produces native crystal growth inhibitors. The macroscopic and microscopic effects imposed by inhibitor-crystal interactions reveal dual mechanisms of inhibition where tautomer occlusion within crystals that leads to natural bending, tunes elastic modulus, and selectively alters the rate of crystal dissolution. Our study focuses on ammonium urate crystallization and shows that the keto-enol form of urate, which exists as a minor tautomer, is a potent inhibitor that nearly suppresses crystal growth at select solution alkalinity and supersaturation. The generalizability of this phenomenon is demonstrated for two additional tautomers with relevance to biological systems and pharmaceuticals. These findings offer potential routes in crystal engineering to strategically control the mechanical or physicochemical properties of tautomeric materials.

6-Methyl-1,3,5-triazine-2,4-diamine butane-1,4-diol monosolvate.

The title co-crystal, C4H7N5·C4H10O2, crystallizes with one mol-ecule of 6-methyl-1,3,5-triazine-2,4-diamine (DMT) and one mol-ecule of butane-1,4-diol in the asymmetric unit. The DMT mol-ecules form ribbons involving centrosymmetric R2(2)(8) dimer motifs between DMT mol-ecules along the c-axis direction. These ribbons are further hydrogen bonded to each other through butane-1,4-diol, forming sheets parallel to (121).

Direct Image Feature Extraction and Multivariate Analysis for Crystallization Process Characterization.

Small-scale crystallization experiments (1-8 mL) are widely used during early-stage crystallization process development to obtain initial information on solubility, metastable zone width, as well as attainable nucleation and/or growth kinetics in a material-efficient manner. Digital imaging is used to monitor these experiments either providing qualitative information or for object detection coupled with size and shape characterization. In this study, a novel approach for the routine characterization of image data from such crystallization experiments is presented employing methodologies for direct image feature extraction. A total of 80 image features were extracted based on simple image statistics, histogram parametrization, and a series of targeted image transformations to assess local grayscale characteristics. These features were utilized for applications of clear/cloud point detection and crystal suspension density prediction. Compared to commonly used transmission-based methods (mean absolute error 8.99 mg/mL), the image-based detection method is significantly more accurate for clear and cloud point detection with a mean absolute error of 0.42 mg/mL against a manually assessed ground truth. Extracted image features were further used as part of a partial least-squares regression (PLSR) model to successfully predict crystal suspension densities up to 40 mg/mL (R 2 > 0.81, Q 2 > 0.83). These quantitative measurements reliably provide crucial information on composition and kinetics for early parameter estimation and process modeling. The image analysis methodologies have a great potential to be translated to other imaging techniques for process monitoring of key physical parameters to accelerate the development and control of particle/crystallization processes.

High spatial resolution ToF-SIMS imaging and image analysis strategies to monitor and quantify early phase separation in amorphous solid dispersions.

Amorphous solid dispersions (ASDs) are formulations with enhanced drug solubility and dissolution rate compared to their crystalline counterparts, however, they can be inherently thermodynamically unstable. This can lead to amorphous phase separation and drug re-crystallisation, phenomena that are typically faster and more dominant at the product's surfaces. This study investigates the use of high-resolution time of flight-secondary ion mass spectrometry (ToF-SIMS) imaging as a surface analysis technique combined with image-analysis for the early detection, monitoring and quantification of surface amorphous phase separation in ASDs. Its capabilities are demonstrated for two pharmaceutically relevant ASD systems with distinct re-crystallisation behaviours, prepared using hot melt extrusion (HME) followed by pelletisation or grinding: (1) paracetamol-hydroxypropyl methylcellulose (PCM-HPMC) pellets with drug loadings of 10%-50% w/w and (2) indomethacin-polyvinylpyrrolidone (IND-PVP) ground material with drug loadings of 20%-85% w/w. PCM-HPMC pellets showed intense phase separation, reaching 100% PCM surface coverage within 1-5 months. In direct comparison, IND-PVP HME ground material was more stable with only a moderate formation of isolated IND-rich clusters. Image analysis allowed the reliable detection and quantification of local drug-rich clusters. An Avrami model was applied to determine and compare phase separation kinetics. The combination of chemical sensitivity and high spatial resolution afforded by SIMS was crucial to enable the study of early phase separation and re-crystallisation at the surface. Compared with traditional methods used to detect crystalline material, such as XRPD, we show that ToF-SIMS enabled detection of surface physical instability already at early stages of drug cluster formation in the first days of storage.

Temperature Correction of Spectra to Improve Solute Concentration Monitoring by In Situ Ultraviolet and Mid-Infrared Spectrometries toward Isothermal Local Model Performance.

Changes in temperature can significantly affect spectroscopic-based methods for in situ monitoring of processes. As varying temperature is inherent to many processes, associated temperature effects on spectra are unavoidable, which can hinder solute concentration determination. Ultraviolet (UV) and mid-infrared (IR) data were acquired for l-ascorbic acid (LAA) in MeCN/H2O (80:20 w/w) at different concentrations and temperatures. For both techniques, global partial least squares (PLS) models for prediction of LAA concentration constructed without preprocessing of the spectra required a high number of latent variables to account for the effects of temperature on the spectra (root mean square error of cross validation (RMSECV) of 0.18 and 0.16 g/100 g solvent, for UV and IR datasets, respectively). The PLS models constructed on the first derivative spectra required fewer latent variables, yielding variable results in accuracy (RMSECV of 0.23 and 0.06 g/100 g solvent, respectively). Corresponding isothermal local models constructed indicated improved model performance that required fewer latent variables in the absence of temperature effects (RMSECV of 0.01 and 0.04 g/100 g solvent, respectively). Temperature correction of the spectral data via loading space standardization (LSS) enabled the construction of global models using the same number of latent variables as the corresponding local model, which exhibited comparable model performance (RMSECV of 0.06 and 0.04 g/100 g solvent, respectively). The additional chemometric effort required for LSS is justified if prediction of solute concentration is required for in situ monitoring and control of cooling crystallization with an accuracy and precision approaching that attainable using an isothermal local model. However, the model performance with minimal preprocessing may be sufficient, for example, in the early phase development of a cooling crystallization process, where high accuracy is not always required. UV and IR spectrometries were used to determine solubility diagrams for LAA in MeCN/H2O (80:20 w/w), which were found to be accurate compared to those obtained using the traditional techniques of transmittance and gravimetric measurement. For both UV and IR spectrometries, solubility values obtained from models with LSS temperature correction were in better agreement with those determined gravimetrically. In this first example of the application of LSS to UV spectra, significant improvement in the predicted solute concentration is achieved with the additional chemometric effort. There is no extra experimental burden associated with the use of LSS if a structured approach is employed to acquire calibration data that account for both temperature and concentration.

Crystal Structure and Twisted Aggregates of Oxcarbazepine Form III.

Polymorphism and crystal habit play vital roles in dictating the properties of crystalline materials. Here, the structure and properties of oxcarbazepine (OXCBZ) form III are reported along with the occurrence of twisted crystalline aggregates of this metastable polymorph. OXCBZ III can be produced by crystallization from the vapor phase and by recrystallization from solution. The crystallization process used to obtain OXCBZ III is found to affect the pitch, with the most prominent effect observed from the sublimation-grown OXCBZ III material where the pitch increases as the length of aggregates increases. Sublimation-grown OXCBZ III follows an unconventional mechanism of formation with condensed droplet formation and coalescence preceding nucleation and growth of aggregates. A crystal structure determination of OXCBZ III from powder X-ray diffraction methods, assisted by crystal structure prediction (CSP), reveals that OXCBZ III, similar to carbamazepine form II, contains void channels in its structure with the channels, aligned along the c crystallographic axis, oriented parallel to the twist axis of the aggregates. The likely role of structural misalignment at the lattice or nanoscale is explored by considering the role of molecular and closely related structural impurities informed by crystal structure prediction.

Precision studies in supramolecular chemistry: a 1H NMR study of hydroxymethoxyacetophenone/ß-cyclodextrin complexes.

The association constants for the interactions of 2-hydroxy-4-methoxyacetophenone, 2-hydroxy-5-methoxyacetophenone, 2-hydroxy-6-methoxyacetophenone, 3-hydroxy-4-methoxyacetophenone and 4-hydroxy-3-methoxyacetophenone with ß-cyclodextrin in water were measured by (1)H NMR and by isothermal titration calorimetry. Very good agreement was obtained between the different methods. The errors associated with the NMR method for measuring mM binding affinities were estimated to be 10-30%, and by isothermal titration calorimetry, 10-20%. Rotating frame nuclear Overhauser effect spectroscopy studies show that the solution phase host-guest complexes formed by ß-cyclodextrin with these hydroxymethoxyacetophenone derivatives are not structurally well defined but that the hydroxymethoxyacetophenone derivatives are mostly associated with the narrow primary hydroxyl rim.

Intermolecular interactions, disorder and twinning in ciprofloxacin-2,2-difluoroethanol (2/3) and ciprofloxacin-water (3/14.5).

The antibiotic ciprofloxacin [systematic name: 1-cyclopropyl-6-fluoro-4-oxo-7-(piperazin-4-ium-1-yl)-1,4-dihydroquinoline-3-carboxylate], has been crystallized as a 2:3 solvate with 2,2-difluoroethanol, 2C(17)H(18)FN(3)O(3)·3C(2)H(4)O(2), (I), and as a 3:14.5 hydrate, 3C(17)H(18)FN(3)O(3)·14.5H(2)O, (II). The structure of (I) was determined using synchrotron X-ray diffraction data and refined as a two-component nonmerohedral twin. Both structures contain several independent molecules in the asymmetric unit: (I) contains two zwitterionic ciprofloxacin molecules and three difluoroethanol solvent molecules, while (II) contains three zwitterionic ciprofloxacin molecules and a mixture of ordered and disordered water molecules. The intermolecular interactions were analysed using fingerprint plots derived from Hirshfeld surfaces, providing a detailed description of the unique environment of each independent ciprofloxacin molecule.

Heat Transfer and Residence Time Distribution in Plug Flow Continuous Oscillatory Baffled Crystallizers.

Heat transfer coefficients in a continuous oscillatory baffled crystallizer (COBC) with a nominal internal diameter of 15 mm have been determined as a function of flow and oscillatory conditions typically used under processing conditions. Residence time distribution measurements show a near-plug flow with high Peclet numbers on the order of 100-1000 s, although there was significant oscillation damping in longer COBC setups. Very rapid heat transfer was found under typical conditions, with overall heat transfer coefficients on the order of 100 s W m-2 K-1. Furthermore, poor mixing in the COBC cooling jacket was observed when lower jacket flow rates were implemented in an attempt to decrease the rate of heat transfer in order to achieve more gradual temperature profile along the crystallizer length. Utilizing the experimentally determined overall heat transfer coefficients, a theoretical case study is presented to investigate the effects of the heat transfer rate on temperature and supersaturation profiles and to highlight potential fouling issues during a continuous plug flow cooling crystallization.

A computationally inspired investigation of the solid forms of (R)-1-phenylethylammonium-(S)-2-phenylbutyrate.

Following the computation of a lattice energy landscape which predicted that there should be more stable, denser forms of (R)-1-phenylethylammonium-(S)-2-phenylbutyrate, crystallizations from a range of solvents were performed to search for other polymorphs and investigate the possibility that the known P4(1) structure could be a hydrate. Extensive crystallization experiments from a wide range of solvents gave fine needles or microcrystalline samples. A redetermination of the P4(1) structure by powder X-ray diffraction located all protons, and in conjunction with other experimental and computational evidence showed that the structure was anhydrous. Evidence for two additional forms was found as mixtures with form I. These include an orthorhombic form, possibly a Z' = 3 polymorph, and another as yet unidentified form obtained as a minor component from dichloromethane solution. However, both these forms appear to be metastable with respect to form I (P4(1)), which is therefore probably the most thermodynamically stable form that can be crystallized from solution under ambient conditions. This determination of the solid state behavior of the less readily crystallized member of the diastereomeric salt system (R)-1-phenylethylammonium-(R/S)-2-phenylbutyrate provides a challenge to the theoretical modeling to explain its ideal resolution behavior.