3.1 Van der Waals forces

Van der Waals forces are weak intermolecular attractions crucial in colloidal systems. They come in three types: Keesom forces between permanent dipoles, Debye forces between permanent and induced dipoles, and London dispersion forces between induced dipoles.

These forces affect particle interactions, stability, and aggregation in colloids. Factors like polarizability, molecular size and shape, and distance between molecules influence their strength. Understanding Van der Waals forces is key to controlling colloidal behavior and designing functional materials.

Types of Van der Waals forces

• Van der Waals forces are weak intermolecular forces that arise from interactions between dipoles in molecules
• These forces play a crucial role in the behavior and properties of colloidal systems, including stability, aggregation, and adsorption
• The three main types of Van der Waals forces are Keesom forces, Debye forces, and London dispersion forces

Keesom forces between permanent dipoles

Top images from around the web for Keesom forces between permanent dipoles

• 

  Chemical Bonds | Anatomy and Physiology I View original

  Is this image relevant?

• 

  Intermolecular Forces | Chemistry: Atoms First View original

  Is this image relevant?

• 

  Intermolecular Forces | Chemistry View original

  Is this image relevant?

• 

  Chemical Bonds | Anatomy and Physiology I View original

  Is this image relevant?

• 

  Intermolecular Forces | Chemistry: Atoms First View original

  Is this image relevant?

1 of 3

Top images from around the web for Keesom forces between permanent dipoles

• 

  Chemical Bonds | Anatomy and Physiology I View original

  Is this image relevant?

• 

  Intermolecular Forces | Chemistry: Atoms First View original

  Is this image relevant?

• 

  Intermolecular Forces | Chemistry View original

  Is this image relevant?

• 

  Chemical Bonds | Anatomy and Physiology I View original

  Is this image relevant?

• 

  Intermolecular Forces | Chemistry: Atoms First View original

  Is this image relevant?

1 of 3

• Occur between molecules with permanent dipole moments (polar molecules)
• Result from the electrostatic attraction between the positive end of one dipole and the negative end of another
• Strength depends on the magnitude of the dipole moments and the mutual orientation of the molecules
• Examples include interactions between water molecules and between acetone molecules

Debye forces between permanent and induced dipoles

• Arise when a permanent dipole induces a dipole moment in a neighboring nonpolar molecule
• The induced dipole is caused by the distortion of the electron cloud in the nonpolar molecule
• Strength depends on the polarizability of the nonpolar molecule and the magnitude of the permanent dipole
• Examples include interactions between water (permanent dipole) and oxygen (induced dipole)

London dispersion forces between induced dipoles

• Present between all molecules, including nonpolar molecules
• Result from instantaneous dipole moments caused by fluctuations in the electron distribution
• Strength depends on the polarizability of the molecules and the number of electrons
• Dominant type of Van der Waals force in most systems
• Examples include interactions between noble gas atoms (helium, neon) and between hydrocarbon molecules

Factors affecting Van der Waals forces

• Several molecular properties and system parameters influence the strength and range of Van der Waals forces
• Understanding these factors is essential for predicting and controlling the behavior of colloidal systems
• The main factors affecting Van der Waals forces are polarizability, size and shape of molecules, and distance between molecules

Polarizability of molecules

• Measure of a molecule's ability to form an induced dipole in response to an electric field
• Increases with the number of electrons and the size of the molecule
• Higher polarizability leads to stronger Van der Waals forces
• Examples of highly polarizable molecules include iodine ($I_2$) and benzene ($C_6H_6$)

Size and shape of molecules

• Larger molecules generally have stronger Van der Waals forces due to increased polarizability
• Shape of the molecule affects the contact area and the packing efficiency
• Elongated or planar molecules (graphene, clay platelets) have stronger interactions compared to spherical molecules
• Size and shape also influence the range of Van der Waals forces

Distance between molecules

• Van der Waals forces are short-range and rapidly decrease with increasing distance
• Strength is proportional to $1/r^6$, where $r$ is the distance between molecules
• Significant only at distances less than a few nanometers
• At very short distances, repulsive forces dominate due to electron cloud overlap (Pauli exclusion principle)

Importance in colloidal systems

• Van der Waals forces play a significant role in the behavior and properties of colloidal systems
• They influence particle-particle interactions, colloidal stability, and aggregation processes
• Understanding the effects of Van der Waals forces is crucial for designing and controlling colloidal formulations

Role in particle-particle interactions

• Van der Waals forces contribute to the attractive interactions between colloidal particles
• Determine the potential energy of interaction as a function of particle separation
• Influence the collision frequency and the likelihood of particle adhesion
• Compete with other forces (electrostatic repulsion, steric hindrance) to determine the net interaction

Contribution to colloidal stability

• Colloidal stability refers to the ability of a dispersion to resist aggregation and sedimentation
• Van der Waals forces promote particle aggregation by providing an attractive force between particles
• Stabilization mechanisms (electrostatic, steric) must overcome Van der Waals attraction to maintain stability
• The balance between Van der Waals attraction and repulsive forces determines the colloidal stability

Influence on flocculation and aggregation

• Flocculation is the process of particle aggregation to form loosely packed clusters (flocs)
• Aggregation refers to the formation of more compact and irreversible particle clusters
• Van der Waals forces drive the initial stages of flocculation and aggregation
• The rate and extent of aggregation depend on the strength of Van der Waals interactions
• Controlling Van der Waals forces is essential for preventing unwanted aggregation or inducing desired flocculation

Comparison with other intermolecular forces

• Van der Waals forces are one of several types of intermolecular forces that govern the behavior of molecules and particles
• It is important to understand the relative strength and characteristics of Van der Waals forces compared to other intermolecular forces
• The main forces to consider are electrostatic forces and hydrogen bonding

Van der Waals vs electrostatic forces

• Electrostatic forces arise from the interaction between charged species (ions, charged particles)
• Can be attractive (opposite charges) or repulsive (like charges)
• Strength depends on the magnitude of the charges and the dielectric constant of the medium
• Electrostatic forces are longer-range than Van der Waals forces and decay as $1/r^2$
• In colloidal systems, electrostatic forces can be used to stabilize dispersions (electrostatic stabilization)

Van der Waals vs hydrogen bonding

• Hydrogen bonding is a specific type of attractive interaction between a hydrogen atom bonded to an electronegative atom (O, N, F) and another electronegative atom
• Stronger than Van der Waals forces but weaker than covalent or ionic bonds
• Highly directional and responsible for the unique properties of water and the secondary structure of proteins
• Hydrogen bonding can compete with or complement Van der Waals forces in colloidal systems

Relative strength of Van der Waals forces

• Van der Waals forces are generally weaker than other intermolecular forces
• Typical strength: 0.4-4 kJ/mol, compared to 12-30 kJ/mol for hydrogen bonds and 250-400 kJ/mol for ionic bonds
• However, the cumulative effect of Van der Waals forces can be significant in colloidal systems due to the large number of particles and the high surface area
• The relative importance of Van der Waals forces depends on the specific system and the presence of other forces

Theoretical models and equations

• Several theoretical models have been developed to describe and quantify Van der Waals interactions
• These models provide a framework for understanding the dependence of Van der Waals forces on system parameters and for predicting the behavior of colloidal systems
• The most widely used models are the Hamaker theory and the Lifshitz theory

Hamaker theory for Van der Waals interactions

• Developed by H.C. Hamaker in 1937

• Calculates the Van der Waals interaction energy between two macroscopic bodies based on the pairwise summation of intermolecular interactions

• For two spherical particles of radii $R_1$ and $R_2$ separated by a distance $D$, the Hamaker equation is: $U(D) = -\frac{A}{6}\left[\frac{2R_1R_2}{D^2-\left(R_1+R_2\right)^2}+\frac{2R_1R_2}{D^2-\left(R_1-R_2\right)^2}+\ln\left(\frac{D^2-\left(R_1+R_2\right)^2}{D^2-\left(R_1-R_2\right)^2}\right)\right]$

• $A$ is the Hamaker constant, which depends on the material properties of the particles and the medium

• Hamaker theory provides a simple and intuitive approach but has limitations for complex systems

Lifshitz theory for macroscopic bodies

• Developed by E.M. Lifshitz in 1956

• Calculates the Van der Waals interaction energy between macroscopic bodies based on the fluctuations of the electromagnetic field

• Considers the dielectric properties of the materials as a function of frequency

• For two semi-infinite half-spaces separated by a distance $D$, the Lifshitz equation is: $U(D) = -\frac{k_BT}{2\pi}\sum_{n=0}^{\infty}{'}\int_0^{\infty}\ln\left[1-\Delta_{12}(i\xi_n)e^{-2k_nD}\right]k_ndk_n$

• $k_B$ is the Boltzmann constant, $T$ is the temperature, $\xi_n$ are the Matsubara frequencies, and $\Delta_{12}$ is a function of the dielectric properties of the materials

• Lifshitz theory is more accurate than Hamaker theory but requires knowledge of the dielectric functions

Limitations and assumptions of models

• Both Hamaker and Lifshitz theories assume continuous media and do not account for atomic structure
• The models are based on linear response theory and may not be valid for strong interactions or high electric fields
• The theories assume that the Van der Waals interactions are additive and do not consider many-body effects
• The accuracy of the models depends on the quality of the input parameters (Hamaker constants, dielectric functions)
• Despite their limitations, these models provide valuable insights into Van der Waals interactions in colloidal systems

Experimental techniques for measuring Van der Waals forces

• Measuring Van der Waals forces experimentally is crucial for validating theoretical models and understanding the behavior of real systems
• Several advanced techniques have been developed to directly measure Van der Waals forces at the nanoscale
• The most common techniques are surface force apparatus (SFA), atomic force microscopy (AFM), and total internal reflection microscopy (TIRM)

Surface force apparatus (SFA)

• Pioneered by J.N. Israelachvili and D. Tabor in the 1970s
• Measures the force between two macroscopic surfaces as a function of their separation
• Surfaces are typically mica sheets coated with a thin layer of the material of interest
• Separation is controlled by a piezoelectric crystal and measured by interferometry
• Sensitivity: forces down to 10 nN, distances down to 0.1 nm
• Allows measurement of both normal and lateral forces
• Provides direct validation of theoretical models for macroscopic bodies

Atomic force microscopy (AFM)

• Developed in the 1980s as a variant of scanning tunneling microscopy
• Measures the force between a sharp tip (radius < 10 nm) and a sample surface
• Tip is attached to a flexible cantilever, and the deflection is measured by a laser and photodetector
• Separation is controlled by a piezoelectric scanner
• Sensitivity: forces down to 10 pN, distances down to 0.1 nm
• Can be operated in various modes (contact, non-contact, tapping) and environments (air, liquid)
• Provides high-resolution force measurements and imaging of surface topography

Total internal reflection microscopy (TIRM)

• Developed by D.C. Prieve and N.A. Frej in the 1990s
• Measures the interaction potential between a colloidal particle and a flat surface
• Particle is suspended in a liquid near a transparent substrate (glass, quartz)
• Evanescent wave is generated by total internal reflection of a laser beam at the substrate-liquid interface
• Scattered light intensity depends on the particle-surface separation
• Sensitivity: distances down to 10 nm, interaction energies down to 0.1 kT
• Allows measurement of weak interactions and particle dynamics near surfaces
• Provides insights into colloidal stability and surface-particle interactions

Applications in colloidal science

• Van der Waals forces have numerous applications in colloidal science and technology
• Understanding and controlling Van der Waals interactions is essential for designing stable and functional colloidal systems
• Some key applications include stabilization of dispersions, control of rheological properties, and design of functional materials and surfaces

Stabilization of colloidal dispersions

• Colloidal dispersions are prone to aggregation due to Van der Waals attraction between particles
• Stabilization requires overcoming Van der Waals forces by introducing repulsive interactions
• Common stabilization mechanisms:
  1. Electrostatic stabilization: adsorption of charged species (ions, surfactants) on particle surfaces
  2. Steric stabilization: adsorption of polymers or nanoparticles that provide a physical barrier
  3. Depletion stabilization: addition of non-adsorbing species (polymers, micelles) that induce repulsive osmotic pressure
• Choice of stabilization method depends on the specific system and the desired properties

Control of rheological properties

• Van der Waals forces influence the rheological properties of colloidal dispersions, such as viscosity, yield stress, and viscoelasticity
• Attractive Van der Waals interactions promote the formation of particle networks and gels, leading to increased viscosity and yield stress
• Controlling Van der Waals forces allows tuning of the rheological properties for specific applications
• Strategies include modifying particle size and shape, changing the medium composition, and adding rheology modifiers (thickeners, thinners)
• Applications include paints, inks, cosmetics, and food products

Design of functional materials and surfaces

• Van der Waals forces can be harnessed to design functional materials and surfaces with specific properties
• Examples include:
  1. Superhydrophobic surfaces: mimicking the hierarchical structure of lotus leaves to achieve high water contact angles and low adhesion
  2. Gecko-inspired adhesives: exploiting the cumulative effect of Van der Waals forces between dense arrays of micro- and nanoscale fibers
  3. Self-assembled monolayers (SAMs): controlling the surface energy and wettability by modifying the terminal groups of adsorbed molecules
  4. Colloidal crystals: using Van der Waals interactions to guide the assembly of particles into ordered structures with unique optical and mechanical properties
• Understanding and manipulating Van der Waals forces opens up new possibilities for the rational design of advanced materials and surfaces