The following systematically explains the essence of ultrafiltration membrane filtration of hydrolyzed proteins from three dimensions: separation mechanisms, mass transfer processes, and membrane-solute interactions.

I. Molecular-Level Separation Mechanisms

1. Physical Essence of Sieving Effect

• Control by Membrane Pore Topology
  Ultrafiltration membranes feature nanoscale interconnected pores on their surface (pore size distribution follows a Log-normal function). When the hydrodynamic radius (R_h) of polypeptide chains in a hydrolyzed protein solution satisfies:
  R_h > r_pore/2
  (where r_pore is the membrane pore radius), steric hindrance causes rejection. Representative calculation example:
  • 10 kDa MWCO membrane ≈ pore size of 4.5 nm
  • Spherical protein: R_h ≈ 0.8 × M^0.33
  • 10 kDa peptide R_h ≈ 2.2 nm → Check: 2.2 nm > 4.5/2 = 2.25 nm? Depends on peptide conformation:
    Linear peptide: R_{h_linear} = 0.15 × M^0.59 → 10 kDa R_h ≈ 4.8 nm > 2.25 nm → Rejection
    Globular peptide: R_{h_globular} = 0.72 × M^0.33 → R_h ≈ 2.2 nm < 2.25 nm → Permeation

2. Quantitative Impact of Electrostatic Interactions

• Membrane Surface Charge Effect
  Polyethersulfone membrane at pH 7 exhibits Zeta potential ≈ -25 mV. Coulombic attraction occurs with positively charged peptides (e.g., those with >30% basic amino acid residues):
  Adsorption energy E_ads ∝ (ζ_m·ζ_p)/εr
  (ζ: potential, ε: permittivity, r: distance)
  This leads to higher rejection than theoretical (e.g., lysozyme hydrolysate rejection in 10 kDa membrane reaches 98% vs. theoretical 85%).

• Donnan Effect
  Fixed charges within membrane pores repel small peptides with like charges:
  Corrected rejection formula: R_actual = R₀ + (1-R₀)·[1-exp(-κ·λ)]
  (κ: inverse Debye length, λ: charge density parameter). The effect becomes significant when conductivity <100 μS/cm.

II. Mass Transfer Kinetics

1. Formation Mechanism of Concentration Polarization Layer

• Boundary Layer Mathematical Model
  A concentration boundary layer forms on the membrane surface with thickness δ. Its concentration gradient follows:
  J_v = D·(dc/dx) - c·v_w
  (J_v: flux, D: diffusion coefficient, v_w: permeation velocity).
  Steady-state solution: c_m = c_b·exp(J_v/k)
  (k: mass transfer coefficient, k = 0.816·(ωD²/L)^1/3, ω: angular velocity, L: flow channel length).

• Gel Polarization Critical Point
  When membrane surface concentration c_m reaches the solubility limit (c_g) of polypeptides:
  J_lim = k·ln(c_g/c_b)
  For hydrolyzed proteins, c_g is typically 200–400 g/L (dependent on hydrophobic amino acid content).

2. Influence of Peptide Conformation on Mass Transfer

• Deformation-Permeation Phenomenon
  Flexible peptide chains (e.g., collagen peptides) elongate under shear flow:
  R_{h_eff} = R_{h_0}·(1+0.5·Wi²)
  (Wi: Weissenberg number, Wi = γ̇·λ, λ: peptide relaxation time)
  This reduces actual rejection molecular weight by 10–30%.

III. Microscopic Mechanisms of Membrane Fouling

1. Molecular Dynamics of Peptide Adsorption

• Hydrophobic Interaction-Dominated Adsorption
  Free energy change between membrane material and hydrophobic regions of peptides (e.g., Pro, Phe, Leu residues):
  ΔG_ads = -π·r²·γ_pm
  (γ_pm: peptide-membrane interfacial tension, typically 20–50 mJ/m²).
  Adsorption amount Γ follows Langmuir model: Γ = Γ_max·K·c/(1+K·c).

• Hydrogen Bond Network Formation
  Hydrogen bonding (bond energy ≈5–25 kJ/mol) forms between membrane hydroxyl/carboxyl groups and peptide amide groups, creating a dense adsorption layer in low-velocity zones.

2. Pore Blocking Classification Mechanism

IV. Energy Analysis of Transmembrane Process

1. Decomposition of Mass Transfer Resistance

Total resistance: R_t = R_m + R_p + R_c

• Membrane inherent resistance R_m: Calculated via Hagen-Poiseuille law: R_m = 32ηL/(εd_pore²)
• Fouling layer resistance R_c: Follows Hermia model R_c = k·Jⁿ·t (n=0–2)
• Concentration polarization resistance R_p: R_p = (RT/D)·(dc/dx) (proportional to concentration gradient).

2. Principle of Energy Minimization

Actual power consumption: P = Q·ΔP/η_pump
Optimization requires satisfying:
Min(P) = f(J_v, v, c_b)
Subject to constraints:

• Peptide rejection ≥90%
• Membrane surface concentration c_m < 0.8 c_g
• Shear rate γ̇ < 10⁵ s^-1 (prevents peptide chain breakage).

V. Strategies for Regulating Molecular Interactions

1. Enhanced Electrostatic Repulsion

• pH Adjustment Window
  Operate at conditions where target peptides and membrane have like charges:
  • Acidic membranes (PES/PVDF): pH > pI + 1.5
  • Basic peptides: pH < pI - 1.5
    (pI determined by CZE with error ±0.1).

2. Steric Hindrance Protection

• Addition of Hydrophilic Polymers
  Polyethylene glycol (PEG6000) forms a hydration layer on the membrane:
  Steric repulsion energy V_steric ≈ 2πkT·a·(δ/d)²
  (a: peptide size, δ: hydration layer thickness, d: distance)
  Reduces adsorption by 30–50%.

3. Regulation of Solvation Effect

• Dielectric Constant Optimization
  Adding ethanol (10–20%) reduces aqueous dielectric constant (ε from 80 to 60), weakening hydrophobic interactions:
  ΔG_hydro ≈ -4πR·(γ_peptide - γ_solvent)²
  (Must control ethanol concentration to prevent peptide denaturation).

Conclusion: Physicochemical Essence of Filtration Process

Ultrafiltration of hydrolyzed proteins is a multi-scale coupled process:

1. Molecular scale: Peptide conformation (rigid/flexible), charge distribution, and hydrophobic patches determine initial adsorption.
2. Nanoscale: Membrane pore topology (pore size distribution, tortuosity factor) controls sieving accuracy.
3. Micron scale: The concentration polarization layer forms a non-equilibrium mass transfer interface.
4. Macroscale: Fluid shear and pressure gradients drive phase separation.

A true understanding requires establishing multi-scale models ranging from quantum chemical calculations (adsorption bond energy) to computational fluid dynamics (boundary layer simulation). This represents the current research frontier and the theoretical foundation for achieving precise separations.