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胶体与表面科学
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胶体与表面科学
12
engines
双电层与 ζ 电位
The electric double layer & zeta potential
双电层Stern+扩散 · ζ滑动面 · |ζ|>30mV稳定/→0凝聚
The Stern + diffuse layer around a colloid, and how ζ at the slipping plane governs sol stability
DLVO 理论:总相互作用能
DLVO theory: total interaction energy
范德华吸引+双电层排斥 · 势能垒vs间距 · 盐升垒降
The sum of van der Waals attraction and double-layer repulsion vs separation D — the barrier sets stability
Schulze–Hardy 规则:临界聚沉浓度与反离子价数
Schulze–Hardy rule: CCC vs counter-ion valence
CCC∝z⁻⁶ · Na:Ca:Al=1:1/64:1/729 · 反离子价
For a negative sol the CCC scales as z⁻⁶, so Al³⁺ ≪ Ca²⁺ ≪ Na⁺ concentrations coagulate it
布朗运动(胶体颗粒的随机行走)
Brownian motion of colloidal particles
随机行走 · ⟨x²⟩=2Dt · D=kT/6πηr · 小粒扩散快
Thermal solvent molecules bombard the particle, driving an endless random walk — Einstein's relation ties it to diffusion
渗透压(半透膜与范特霍夫定律)
Osmotic pressure across a semipermeable membrane
π=iMRT · 半透膜 · 海水~48bar · 反渗透
Solvent crosses the membrane toward the concentrated side until the column it raises balances it — that is the osmotic pressure π = i·M·R·T
丁达尔效应(胶体对光的散射)
The Tyndall effect (light scattering by colloids)
Rayleigh∝1/λ⁴ · 蓝比红散射5.9× · 胶体vs溶液
A beam through a colloid is scattered sideways into a visible path; a true solution does not scatter — that is how you tell them apart
临界胶束浓度(CMC)
Critical micelle concentration (CMC)
CMC突变 · 表活剂自组装 · SDS 8.2mM · 表面张力拐点
Surfactants self-assemble into micelles at the CMC — many properties break slope there
杨-拉普拉斯方程(曲面附加压强)
Young–Laplace equation (curved-interface pressure)
ΔP=2γ/r · 小滴内压高 · 肥皂泡4γ/r · 1µm→1.44bar
A curved interface holds a pressure jump ΔP = 2γ/r (droplet); a soap bubble has two surfaces, ΔP = 4γ/r
润湿与接触角(杨氏方程)
Wetting & contact angle (Young's equation)
cosθ=(γsv−γsl)/γlv · <90润湿/>90疏水/>150超疏水
Three interfacial tensions balance at the contact line: cosθ = (γsv − γsl)/γlv; θ sets the wetting regime
朗缪尔吸附等温线
Langmuir adsorption isotherm
θ=KP/(1+KP) · P=1/K半覆盖 · 单层饱和
Monolayer adsorption: coverage θ saturates at one layer, θ = K·P /(1 + K·P)
BET 多层吸附与比表面积
BET multilayer adsorption & surface area
多层BET · 线性式取Vm · 比表面积 · N2 σ=0.162nm²
Multilayer physisorption: extract monolayer capacity Vm by BET linear plot, then surface area S
吉布斯吸附等温式
Gibbs adsorption isotherm
Γ=−(1/RT)dγ/dlnC · 表面过剩 · 分子面积0.41nm²
The steeper γ falls, the larger the surface excess Γ: Γ = −(1/RT)·dγ/dlnC