4: Sorption into Colloidal Particles

a phenomenon in which ions and molecules are bound to the surface of solid particles such as oxides and clay minerals

a phenomenon in which ions and molecules are allowed to penetrate and bind to internal sites of more permeable particles such as humic substances

the general term embodying the phenomena of adsorption and absorption

an equilibrium relationship between the activity (or fugacity) of the sorbate in the bulk phase and the activity of the bound sorbate

the species (ions and molecules) to be bound

the solid phase constituent participating in a sorption reaction

the amount of adsorbate bound in terms of surface excess/concentration or molality, (moles of sorbate per unit mass of sorbent): $Q_A=\frac{n_A}{m_S}=\Gamma_AA_S$

the relative amount of adsorbate bound: $\theta_A=\frac{\Gamma_A}{\Gamma_S}=\frac{Q_A}{Q_S}$, where $\Gamma_S$ and $Q_S$ represent the maximum amount bound in a single layer covering the surface (saturation coverage, number of sites per unit area, or site density)

5 classifications provided by Brunauer et al.; each is identified by a distinct isotherm whose relevant independent variable is the gas pressure (or adsorbate partial pressure, considering ideal behavior of the gas); for type I: $\mu_\text{ideal gas} (T,P) = \mu^0_\text{ideal gas} + RT \ln \frac{P}{P^0}$, where $\mu^0$ is the standard chemical potential and $P^0$ the standard pressure

in gas phase, adsorption molecules from the gas hit the surface on empty sites where they may eventually get bound; in a solution, solvent molecules are present almost everywhere so that the adsorption of a solute molecule is actually an exchange process between solvent and solute

physisorption (nonspecific adsorption), chemisorption (specific adsorption)

$\Delta H_{ad}$, the enthalpy change upon desorption (although always reported as positive since clearly adsorption is exothermic and desorption is endothermic)

in physisorption processes, it is relatively low, similar to vaporization enthalpies: argon on graphite is $\Delta H_{ad} \approx 11$ kJ/mol whereas chemisorption processes have higher heats, typically by one order of magnitude: $N_2$ on iron at high temp (400C) is $\Delta H_{ad} \approx 209$ kJ/mol

physisorption has no activation energy, in principle; chemisorption is a chemical reaction with an energy of activation so that at low temperatures, the adsorbing molecules are unable to overcome the activation barrier, kinetically preventing the process

yielded from sorbate reaching close contact with the surface, losing either totally or partially its hydration layer

yielded from sorbate separated from the surface by at least one layer of water molecules, retaining its hydration layer

specific adsorption implies inner-sphere complex, but the opposite is not true. In an outer-sphere complex, the adsorbate is separated from the surface for at least one layer of water molecules, preventing any type of bonding, thus this is always nonspecific adsorption; on the other hand, an adsorbate in an inner-sphere complex may form some sort of chemical bond, but not necessarily, e.g., K+ ions in micas are often found as inner-sphere complexes, but interaction is mainly electrostatic & no chemical bond is formed

governed by Coulomb's law: $u_{I-I}(r)=\frac{q_1q_2}{4 \pi ε r}$ where $u_{I-I}$ is the energy of interaction between two ions, $q_1$ and $q_2$ are the respective charges, ε is the medium permittivity and r the distance between them; notice the exponent on r: these are long-range interactions

assuming dipole rotation freedom, $u_{I-D}(r)=- \frac{|q_1|p_2}{4 \pi ε r^2}$, where $p_2$ is the dipolar moment of a dipole; notice the exponent on r: these are shorter range interactions than ion-ion

the sum of Keesom, Debye and London interactions, the weight of each contribution depending on the particular molecule; the overall magnitude is similar to that of ion-dipole interactions; notice the exponent on r in each case: these are short-range interactions

$u_K(r)=- \frac{2}{3kT} \left( \frac{p_1p_2}{4 \pi ε} \right)^2 \frac{1}{r^6}$, occurring when dipoles rotate due to thermal agitation but, due to mutual interaction, having, on average, attractive orientations (opposite charges facing each other)

$u_D(r)=- \frac{p^2_1 \alpha_2}{(4 \pi ε)^2r^6}$, occurring when a polar and nonpolar molecule are in proximity, the first inducing a transient dipole in the second, giving rise to a permanent dipole-induced dipole interaction; if two permanent dipoles interact, each one will induce a transient dipole on the other, resulting in $u_D(r)=- \frac{p^2_1 \alpha_2 + p^2_2 \alpha_1}{(4 \pi ε)^2r^6}$

also known as induced dipole-induced dipole, these interactions arise from quantum mechanical results for a system composed of two "vibrating dipoles" due to symmetrical vibration of electrons; given approximately by $u_L(r)=- \frac{3h \nu_1 \nu_2 \alpha_1 \alpha_2}{2( \nu_1 + \nu_2)(4 \pi ε)^2 r^6}$, where $\nu_1$ and $\nu_2$ are the frequencies of oscillation of the electrons for the free (noninteracting) molecules and h is Planck's constant

$\frac{h \nu_1 \nu_2}{\nu_1 + \nu_2} \approx \frac{I_1I_2}{I_1+I_2}$

$u_{A-S}(d)=-\frac{\pi u'_{A-B} \rho_B}{6d^3}$, the interaction of molecule A with the surface of a solid formed by molecules B

at short distances, a repulsive interaction arises due to the overlapping of the electronic clouds; this is nearly exponential but is often approximated by a term of the form $u''/r^n$ with $n>9$; in the Lennard-Jones potential, it is taken as 12 for mathematical convenience

if particles (molecule, ion or colloid) are farther apart, there is a time retardation (equivalent to a phase lag) between the vibrations of both the bodies, the importance of which increases as the distance approaches the wavelength of the electric field: $r \rightarrow \lambda$; the result is that, for $r \gg \lambda$, $u_R(r)= \frac{23hc \alpha_1 \alpha_2}{8 \pi^2(4 \pi ε)^2r^7}$; measurements show the crossover from $r^{-6}$ to $r^{-7}$ occur in the range 10-100 nm, which is only important when considering interactions between macroscopic particles

Coulombic interactions are strong and long-range; however, in a medium of high dielectric constant like water ($ε_r \approxeq 78$) and in the presence of dissolved ions that screen the interactions, its relative importance is strongly reduced, becoming comparable to dipolar interactions

$K_AP_A=\frac{k_{ads}}{k_{des}} P_A \equiv \frac{\theta_A}{1- \theta_A} \equiv \frac{\Gamma_A}{\Gamma_S - \Gamma_A} \equiv \frac{Q_A}{Q_S-Q_A}$, where $K_A=\frac{\alpha e^{- \frac{\Delta H_{ads}}{RT}}}{\beta \Gamma_S \sqrt{2 \pi M_r RT}}$

the fitting to one or another isotherm equation in general tells little about the molecular nature of the particular adsorption process