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Related Concept Videos

Phase Diagrams02:39

Phase Diagrams

41.8K
A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Phase Diagram01:19

Phase Diagram

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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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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...
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pV-Diagrams01:18

pV-Diagrams

4.2K
The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
4.2K
Polymer Classification: Crystallinity01:21

Polymer Classification: Crystallinity

2.9K
Unlike ionic or small covalent molecules, polymers do not form crystalline solids due to the diffusion limitations of their long-chain structures. However, polymers contain microscopic crystalline domains separated by amorphous domains.
Crystalline domains are the regions where polymer chains are aligned in an orderly manner and held together in proximity by intermolecular forces. For example, chains in the crystalline domains of polyethylene and nylon are bound together by van der Waals...
2.9K
Molecular Weight of Step-Growth Polymers01:08

Molecular Weight of Step-Growth Polymers

2.2K
Step growth polymerization involves bi or multifunctional monomers. Bifunctional monomers react to form linear step growth polymers, whereas multifunctional monomers react to form non-linear or branched polymers.
As the step-growth polymerization involves step-wise condensation of monomers, the molecular weight also builds up eventually. Consequently, high molecular weight polymers are obtained at the late stages of the polymerization, where 99% of monomers have been consumed.
The extent of the...
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Fluctuation-Corrected Phase Diagrams for Diblock Copolymer Melts.

Mark W Matsen1,2,3, Tom M Beardsley1, James D Willis2

  • 1Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.

Physical Review Letters
|June 30, 2023
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Field-theoretic simulations reveal fluctuation corrections in diblock copolymer melts. These corrections shift the order-disorder transition and stabilize network phases, explaining experimental observations.

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Area of Science:

  • Polymer Science
  • Materials Science
  • Computational Chemistry

Background:

  • Self-consistent field theory (SCFT) is a standard model for polymer behavior.
  • Conventional simulations of SCFT are computationally limited, especially for diblock copolymer melts.
  • Understanding phase transitions and stability in copolymer systems is crucial for materials design.

Purpose of the Study:

  • To evaluate fluctuation corrections to SCFT using advanced field-theoretic simulations (FTSs).
  • To determine complete phase diagrams for diblock copolymer melts with varying polymerization indices.
  • To explain experimental observations of phase stability, including the Fddd phase.

Main Methods:

  • Utilized new developments in field-theoretic simulations (FTSs).
  • Calculated phase diagrams for a series of invariant polymerization indices.
  • Incorporated fluctuation corrections beyond the mean-field approximation.

Main Results:

  • Fluctuations stabilize the disordered phase, shifting the order-disorder transition (ODT) to higher segregation.
  • Network phases are stabilized at the expense of the lamellar phase due to fluctuations.
  • The Fddd phase observed in experiments is accounted for by these stabilization effects.

Conclusions:

  • Fluctuation corrections are essential for accurately predicting phase behavior in diblock copolymer melts.
  • Undulation entropy, favoring curved interfaces, likely explains the stabilization of network phases.
  • FTSs provide a powerful tool for exploring complex copolymer phase diagrams beyond conventional simulation limits.