Adhesion Created 2026-10-20 Updated 2026-11-05
Adhesion is attraction between different surfaces that can keep them attached after a compressive contact load is removed. It can arise from intermolecular forces or other interfacial interactions; a liquid bridge can also contribute a capillary force. The work needed to reversibly separate a unit area is an interfacial energy, whereas the measured pull-off force depends additionally on geometry and elastic deformation.
Pressing a spherical probe onto a specimen and then retracting it provides a direct test. Contact may persist while the apparatus reads a tensile force; detachment occurs only when that adhesive contact becomes unstable. Hertzian contact cannot describe this tensile branch because it neglects adhesion. Surface contamination, roughness and humidity can change a measurement even when the bulk Young's modulus stays fixed. This makes preparation of the interface as important as calibration of the force probe when comparing adhesive response.
Cocrystal Created 2026-10-20 Updated 2026-11-05
A cocrystal is a single crystalline phase containing two or more distinct molecular components in a shared ordered structure. Its components occupy defined roles in the repeating arrangement, rather than simply forming separate crystals mixed together. A stylized arrangement of molecules A and B illustrates the idea without assuming that every cocrystal has that ratio.
Intermolecular forces and molecular geometry influence which combined structure is favorable. A diffraction measurement tests the shared ordering, while a phase diagram distinguishes a stable combined phase from coexistence of separate A-rich and B-rich phases. This is useful because a shared lattice can change properties such as melting behavior and mass density even though the identities of the molecular components remain recognizable. The word describes a structural phase assignment and does not by itself predict which component combinations will form one.
Crystal packing Created 2026-10-20 Updated 2026-11-05
Crystal packing describes how constituents are arranged and make contact within a crystal. It includes both the repeated geometry and, for molecular crystals, the orientations and intermolecular contacts of the molecules. Composition alone does not determine this arrangement: the same substance can have different crystal polymorphs with different packing.
A useful geometric model replaces constituents by equal hard spheres. Hexagonal close packing and face-centered cubic packing put each sphere next to twelve nearest neighbours but arrange successive close-packed layers differently. Their local contact geometry can therefore agree while their longer-range order differs. Real molecular shapes and directional intermolecular forces supply further constraints. Packing affects mass density, available slip geometry and directional response, making diffraction a way to connect structural measurements with macroscopic properties rather than merely assign a repeating pattern.
Past exam of the physics B course of the University of Cambridge 2012 Paper 2 Section A A1 Solution 2026-10-20
For the one-mole convention, is the excluded molar volume: finite molecular size reduces the volume available for translational motion from to . It is an effective excluded volume, not simply the sum of the bare molecular volumes. corrects for attractive intermolecular forces, which reduce the pressure exerted on the wall. The attraction per molecule scales with number density, and the number of affected molecules also scales with density, producing the density-squared correction. The Van der Waals equation consequently raises the measured pressure to the corresponding repulsive-gas value before multiplying by the available volume. Both corrections vanish relative to the ideal-gas terms at sufficiently low density.
Quadrupole interaction Created 2026-10-20 Updated 2026-11-05
An electrostatic interaction involving an electric quadrupole moment, the second-order term in a multipole expansion. About a specified origin, use the conventionHere is an electric charge, its position, and the Kronecker delta. Far from the electric charges, the quadrupole contribution to electrostatic potential iswhere is vacuum permittivity. Thus a point electric charge has quadrupole interaction potential energy proportional to at fixed orientation. A second electric quadrupole moment couples to second derivatives of this electrostatic potential, giving quadrupole–quadrupole potential energy proportional to at fixed orientations. These are far-field terms, rather than the whole intermolecular force at close contact.
Benzene has no permanent electric dipole moment by symmetry, but its electric quadrupole moment need not vanish. Its electrostatic interaction therefore depends on the relative molecular orientations even without permanent electric dipole moments. Published electric quadrupole moment conventions can differ by a factor of two; the tensor convention above must be matched before inserting tabulated values.[ref]
Electric quadrupole moments in the CCCBDB by National Institute of Standards and Technology. Tutorial: Primitive? Traceless?; experimental quadrupoles: benzene entry; far-field powers derived here from the multipole expansion