Suspensions PDF

Types of Intermolecular Forces Between Molecules or Ions 3 Review: for dispersions of particles in a liquid Three general physical instability problems 1. Non-wetting. Solid particles don’t disperse uniformly when placed into the liquid (e.g. addition of surfactants to the liquid can help improve...

Types of Intermolecular Forces Between Molecules or Ions 3 Review: for dispersions of particles in a liquid Three general physical instability problems 1. Non-wetting. Solid particles don’t disperse uniformly when placed into the liquid (e.g. addition of surfactants to the liquid can help improve wetting properties of solid particles) 2. Aggregation/Coalescence. Particles aggregate to form larger agglomerates or, if liquid-liquid or vapor-liquid, they coalesce. 3. Sedimentation/Creaming. Particles (liquid, vapor, solid) sediment or cream due to gravitational effects and density differences. All of these phenomena lead to non-uniformity of particle dispersion within the liquid. 4 Strength of particle interactions • Encounters between particles occurs as a result of Brownian motion (aka, random motion of particles due to collisions with liquid molecules) • Stability of a suspension depends on the types of interactions between particles during these encounters. This stability depends on the balance of attractive & repulsive interactions. Attraction between particles occur due to Van der Waals forces Repulsion between like particles occur due to electrostatic forces. 5 Particle Agglomeration • When particles are dispersed into a liquid, a large interfacial area (∆A) is created. Since ∆G = γ ∆A, the overall free energy of the system increases making the system thermodynamically unstable. • Results in highly “energetic” particles • Since ΔG > 0, the area should spontaneously decrease to lower ΔG thereby leading to phase separation. i.e. Particles want to decrease the available surface area exposed to the liquid by regrouping and forming an agglomerate:  Floccules  Aggregates Particle attraction: Flocculation • An unstable formation of agglomeration from a coarse suspension • Particle attraction through weak Van der Waals intermolecular forces forming light, fluffy structures Particle attraction: Aggregation • Particle attraction through stronger intermolecular forces (e.g. electrostatic) • What defines “colloidal stability”? Solns = thermodynamically stable, coarse dispersions=unstable Particles do not aggregate, particles tend to aggregate • To prepare stable dispersions, thermodynamic tendency (ΔG > 0) must be overcome by protecting particles against aggregation by introducing repulsive interactions Particle-Particle Attraction • At a certain distance (d), nonpolar molecules feel attractive forces due to Van der Waal forces Two spheres are distance (d) apart −Aa Ea = 12d Ea: a: A: + Energy (E) d Energy of attraction curve is used to describe the variation in van der Waals force with distance between the particles - Energy of attraction Particle radius Hamaker constant, characteristic of the system d Particle Number -> Probability • More particles per unit volume of dispersion • More probability of particle interactions (attraction/repulsion) Question ? • How can the formation of a hard cake be prevented over a long period of time? Answer: • Place a “repulsive” or “shielding” barrier on the particle What sort of “repulsive” barriers? Steric and/or electrical. Steric Repulsive Barrier • A repulsive barrier by adsorbing a long chain polymer or other large macromolecules onto the surface. steric repulsion • Polymer chains don’t mix well and thus particles cannot approach each other.  Nonionic polymers such as PEG work well: Not sensitive to surface charge and salt conc. Works well in non-aqueous media Works in concentrated dispersions Electric Repulsive Barriers - - - - - - - - - - - - - - - - - - - A single type of charge is not desired but rather electroneutrality. - - - + - + +- + - - + + CHARGE - SEPARATION + + + - Since counterions can move around and the neg. charges are fixed, there is an electric field in the surface vicinity. + - 11 Electric Repulsive Barriers The greater the number of charges on the surface per unit area, the stronger will be the repulsion. +E, repulsive + Energy (E) # charges is greater - less d -E, attractive Combination of Attractive/Repulsive Forces Energy (E) Energy (E) + + d d - - primary minimum secondary minimum Primary Minimum Secondary Minimum • Irreversible attraction • Reversible attraction • Deflocculated systems • Flocculated systems 13 Potential Energy Diagram (DLVO Theory) Repulsive energy is proportional to size of particles repulsion Second energy minimum, flocculation attraction Primary energy minimum, aggregation Fig. 17-1 in Physical Pharmacy Zeta Potential is a measure of the surface potential of particles • • • Specifically measures “The diffuse layer” around a charged particle and is the difference in potential energy between the inner layer of tightly bound ions and the electroneutral region of the solution Is a surface charge gradient Zeta potential (ζ) is a variable depending on the sign and number of charges at the surface (e.g., -200 mV, +150 mV) Electrical Sensitivity Electrical repulsion between particles is sensitive to: • • • Counterions in solution Concentration of ions Valence of ions Counterions • The presence of counterions tends to screen the repulsive effects of the fixed charges on the surface. • Counterions act as “screening electrolytes” • The more charge per counterion “Higher Valence”, the greater the “Screening Effect” at the same concentration.  (-): charged surface effects, Na+ < Ca2+ < Al3+  (+): charged surface effects, Cl- < SO42- < PO43- Consider The Following…… A particle with a surface (+) charge in an electroneutral ionic solution. i.e. Equal distribution of (+) and (-) ions in the bulk Negative ions in solution will be attracted to the Positive surface/interface. These ions are called Counterions or Gegenions The layer of counterions at the solid surface is called the Stern Plane or Stern Layer. This is a tightly associated layer of ions. i.e. The shear plane is edge of Stern layer, not the solid surface - -- - - - - The Electric Double Layer - + - - + + - + - - - - - - - +- + + - - + -+ + + - - - - + - + - + - - + - - + + The attraction of the counterions to the solid surface and the repulsion of coions (same charge as the surface) form a gradient of ions outside the stern plane. In this case, more (-) ions that diffuse out to neutrality What is the Potential? Nernst Potential: Charge at the solid surface. “PotentialDetermining Ion” Zeta-Potential: Overall Charge at the boundary of the Stern plane (shear plane). Different than the Nernst potential due to the attracted counterions. Zeta can be lower in magnitude to the Nernst or opposite, depending on amount of absorbed counter-ion Ion distribution beyond the double layer is the same as the bulk. Electroneutral!! Zeta-potential is dependent on the amount counterion Potential (+) + 0 Counterion neutralizes surface charge Total Charge of counterion exceeds the potential-determining ions. Total Charge of counterion is less than the potential-determining ions. (-) - Reality… - solvent is bound to the particle and moves with it within this plane • Note: to date, people do not know the actual position of the shear plane. Conventionally, it is thought that the shear plane is very close to the Stern plane. • Zeta potential is actually a measurement at the shear plane Importance of Zeta Potential • Zeta Potential (or charge of the dispersed particle) is important in stability of the system. • Charge repulsion between like charged particles, prevents particle interactions that can lead to instability. E.g. Flocculation, Coalescence • Zeta potential of the particle and ultimately the stability of the system can be greatly affected by electrolytes, pH, and other molecules that can adsorb to the interface! Deflocculated System = charged particles (different size) time gravity Hard cake formation Deflocculated particles: Particles reside in primary minimum • Have a high zeta potential • Repulsive forces exceed attractive forces • Settle slowly, large particles then smaller ones, forms a close-packed arrangement • Has a “pleasing appearance” (supernate remains cloudy) • Eventually forms a sediment in which aggregation occurs (caking) • Difficult to re-suspend once caked 23 = ion Flocculated System time = charged particles (different size) gravity Loose structural flocs Flocculated particles are: • • • • • • • Approaching particles reside in secondary minimum Have a lower zeta potential Forces of attraction predominate over repulsive forces Addition of counterions/steric barriers act as a bridge between particles = weakly bonded particles Settle rapidly Have an “unsightly appearance” (supernatant is clear) Does not form a cake Are easily re-suspended 24 Sedimentation Parameter F • F = sedimentation volume (normal range from 0-1) Vu F= Vo F = 1 (flocculation equilibrium) Vu = final volume (or height) of sediment Vo = original volume (or height) of the suspension before settling 25 How to control flocculation • Start with deflocculated + charged particles in solution • Bring about flocculation by adding electrolytes and/or polymers – e.g. as KH2PO4 conc. is increased, note the decreasing zeta potential • Aim - add an appropriate amount of flocculating agent to result in the maximum sedimentation volume F 26 Sedimentation & Creaming 1) Place a spherical particle into a liquid 2) If the particle has a greater density than the liquid, it will “sediment” to the bottom. If the particle has less density than the liquid, it will “float” or “cream.” 3) In both cases we are seeing separation of phases caused by gravitational forces. sedimentation creaming The Stokes Equation: rate of sedimentation/creaming 2a ⋅ (ρ p − ρ m )⋅ g 2 v= • • • 9η v ∝ a2 (particle size is very important) If ρp = ρm, then v = 0 (one way to slow down movement) v ∝η-1 η = viscosity ρm = liquid density a = particle radius g = 9.8 m/s2 ρp = particle density Limitation of Stokes Equation Applies only to: • Spherical particles in a very dilute suspension (0.5 to 2 gm per 100 ml, <2% w/v). • Particles which freely settle without interference with one another (without collision). • Particles with no physical or chemical attraction or affinity with the dispersion medium. Most pharmaceutical suspension formulation has conc. 5%, 10%, or higher percentage, so there is actually hindrance in particle settling. 33 Settling in suspensions containing high percentage of solids follows a modification of Stokes’ Law (i.e., hindered settling): v ′ = vε n v' = rate of fall at the interface (cm/sec) v = velocity of sedimentation from Stoke’s Law ε = initial porosity of the system n = a measure of the “hindering” of the system (a constant for each system) 34