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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
Phase Diagrams of Ternary Systems01:28

Phase Diagrams of Ternary Systems

Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
X-ray Diffraction of Biological Samples01:10

X-ray Diffraction of Biological Samples

X-ray diffraction or XRD is an analytical tool that utilizes X-rays to study ordered structures such as crystalline organic and inorganic samples, polycrystalline materials, proteins, carbohydrates, and drugs.
According to Bragg's law, when X-rays strike the sample positioned on a stage, the rays are  scattered by the electron clouds around the sample atoms. The  X-ray diffraction or scattering is caused by constructive interference of the X-ray waves that reflect off the internal crystal...

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Related Experiment Video

Updated: May 9, 2026

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
08:55

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Detecting phase separation of freeze-dried binary amorphous systems using pair-wise distribution function and

Norman Chieng1, Hjalte Trnka, Johan Boetker

  • 1Department of Pharmacy, Faculty of Health and Medical Sciences, University of Copenhagen, 2100 Copenhagen, Denmark. norman_chieng@imu.edu.my

International Journal of Pharmaceutics
|July 23, 2013
PubMed
Summary

Multivariate data analysis of powder X-ray diffraction-pair-wise distribution function (PXRD-PDF) data effectively detects phase separation in freeze-dried amorphous systems. This approach offers clearer interpretations than traditional methods and aligns with differential scanning calorimetry findings.

Keywords:
Freeze-dryingPair-wise distribution functionPhase separationPowder X-ray diffractionPrincipal component analysis

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Last Updated: May 9, 2026

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Area of Science:

  • Materials Science
  • Analytical Chemistry
  • Physical Chemistry

Background:

  • Freeze-drying is crucial for creating amorphous systems, but understanding their phase behavior is complex.
  • Detecting phase separation in binary amorphous systems is vital for formulation stability and performance.
  • Traditional methods for analyzing phase separation can be ambiguous.

Purpose of the Study:

  • To investigate the application of multivariate data analysis on powder X-ray diffraction-pair-wise distribution function (PXRD-PDF) data.
  • To develop a robust method for detecting phase separation in freeze-dried binary amorphous systems.
  • To compare the efficacy of this novel approach with established techniques like differential scanning calorimetry (DSC).

Main Methods:

  • Freeze-drying of polymer-polymer and polymer-sugar binary systems at various compositions.
  • Analysis of samples using powder X-ray diffraction (PXRD) and transformation to pair-wise distribution function (PDF) data.
  • Application of principal component analysis (PCA) to PXRD-PDF data for pattern recognition and classification.
  • Validation of results using differential scanning calorimetry (DSC) to determine glass transition temperatures (Tg').

Main Results:

  • Principal Component Analysis (PCA) of PXRD-PDF data provided clear distinctions between miscible and phase-separated systems.
  • Phase-separated systems showed samples distributed evenly around the theoretical PDF profile.
  • Miscible systems exhibited a distinct deviation of samples from the theoretical PDF profile.
  • PCA allowed for simultaneous analysis of replicate samples, enhancing efficiency.
  • The PXRD-PDF-PCA method's phase behavior analysis results were consistent with DSC findings.

Conclusions:

  • The combined PXRD-PDF-PCA approach offers an improved and clearer interpretation of PXRD-PDF data for phase separation detection.
  • This method serves as a valuable alternative explorative data analytical tool for binary amorphous systems.
  • The study successfully demonstrates the utility of multivariate analysis in characterizing complex material behaviors.