Determination of Leaf Water Potential ($Psi_w$) via the Chardakov Density-Gradient Falling-Drop Method
Water potential ($Psi_w$) represents the free energy or chemical potential of water per unit volume relative to pure free water at standard atmospheric pressure and temperature ($Psi_w^circ = 0text{ MPa}$). In plant cells, total water potential is governed by the thermodynamic relationship:
$$Psi_w = Psi_s + Psi_p + Psi_m$$
where $Psi_s$ is osmotic (solute) potential (always negative or zero), $Psi_p$ is turgor (pressure) potential (positive in turgid cells, zero at incipient plasmolysis), and $Psi_m$ is matric potential (negligible in fully hydrated vegetative cells).
Chardakov’s Principle of Density Gradients: When plant tissue is incubated in an external sucrose solution:
1. Hypotonic Solution ($Psi_{text{sol}} > Psi_{text{tissue}}$): Water moves down its free energy gradient by osmosis from the solution into the tissue. As water is removed, the external sucrose solution becomes more concentrated and its physical density ($rho$) increases. When a drop of the unincubated control solution (tinted with methylene blue) is released into this test tube, the control drop is lighter and floats upward ($uparrow$).
2. Hypertonic Solution ($Psi_{text{sol}} < Psi_{text{tissue}}$): Water moves out of the tissue into the solution. The solution becomes diluted and its density decreases. The tinted control drop is denser and sinks downward ($downarrow$).
3. Isotonic Solution ($Psi_{text{sol}} = Psi_{text{tissue}}$): There is no net movement of water ($Delta text{Volume} = 0$). The density of the test solution remains identical to the control solution. The tinted drop neither rises nor sinks; it diffuses symmetrically / hovers stationary in place.
At this isotonic equilibrium point, the water potential of the tissue is equal to the osmotic potential of the sucrose solution, calculated via the van ‘t Hoff equation:
$$Psi_w = Psi_s = -i cdot M cdot R cdot T$$
where $i$ is the ionization constant ($1.0$ for non-ionizing sucrose), $M$ is sucrose molarity ($text{mol/L}$), $R$ is the universal gas constant ($0.008314text{ MPa}cdottext{L}cdottext{mol}^{-1}cdottext{K}^{-1}$), and $T$ is absolute temperature in Kelvin ($T = 273.15 + t^circtext{C}$).
- Plant Tissue: Uniform tissue cylinders cut with a $7.0text{ mm}$ cork borer from fresh potato tubers (*Solanum tuberosum*), sliced into uniform $2.0text{ mm}$ discs.
- Graded Sucrose Series: $1.0text{ M}$ primary analytical sucrose stock diluted into 8 graded test solutions: $0.05$, $0.10$, $0.15$, $0.20$, $0.25$, $0.30$, $0.35$, and $0.40text{ M}$.
- Color Indicator: Crystalline Methylene Blue (or $1% w/v$ aqueous solution) to dye the reference series without altering solution density ($< 0.01% w/v$).
- Glassware: Two matched sets of 8 test tubes (Set A: Test tubes with tissue; Set B: Control reference tubes without tissue), test tube racks, and fine-tip Pasteur pipettes.
Label two matched sets of 8 test tubes ($0.05text{ M}$ through $0.40text{ M}$). Dispense precisely $10.0text{ mL}$ of each sucrose solution into the corresponding tubes of both Set A (Experimental) and Set B (Control). Add a trace amount of methylene blue powder (approx. 1 mg) to each tube in Control Set B to impart a clear blue tint.
Cut 80 uniform potato discs ($2text{ mm}$ thickness, $7text{ mm}$ diameter). Rinse briefly in distilled water to wash off broken cell starch and blot dry on filter paper. Place exactly 10 discs into each tube of Experimental Set A. Stopper all tubes and incubate at room temperature ($22^circtext{C}$) for 90 minutes with gentle swirling every 15 minutes.
Remove potato discs from Set A. Draw a small volume of tinted control solution from Tube B (e.g., $0.05text{ M}$) into a fine-tip Pasteur pipette. Immerse the pipette tip halfway into the corresponding Experimental Tube A ($0.05text{ M}$) and carefully release a single tiny blue droplet (~$10 mutext{L}$) into the center of the column. Observe droplet movement against a white background: record whether the drop rises (↑), sinks (↓), or hovers stationary (•).
Identify the exact molarity where the drop remains stationary. If stationary behavior lies between two tested concentrations, record the midpoint. Apply the van ‘t Hoff equation to calculate total leaf/tuber water potential in MegaPascals (MPa).
| Sucrose Molarity (M) | Theoretical Ψ_sol at 22°C (MPa) | Observed Drop Behavior | Direction of Water Flow | Inference |
|---|---|---|---|---|
| 0.05 M | −0.123 MPa | Rapidly sinks ↓ (Fast) | Solution → Tissue (Swelling) | Hypotonic (Ψ_sol > Ψ_tissue) |
| 0.10 M | −0.245 MPa | Sinks ↓ (Moderate) | Solution → Tissue | Hypotonic |
| 0.15 M | −0.368 MPa | Slowly sinks ↓ | Solution → Tissue | Hypotonic |
| 0.20 M | −0.491 MPa | Barely drifts down ↓ | Slight influx | Near equilibrium |
| 0.25 M | −0.613 MPa | STATIONARY • Hovers in place | No Net Movement (ΔV = 0) | ISOTONIC POINT (Ψ_w = Ψ_sol) |
| 0.30 M | −0.736 MPa | Slowly rises ↑ | Tissue → Solution (Efflux) | Hypertonic (Ψ_sol < Ψ_tissue) |
| 0.35 M | −0.859 MPa | Rises ↑ (Moderate) | Tissue → Solution | Hypertonic |
| 0.40 M | −0.982 MPa | Rapidly floats ↑ (Fast) | Tissue → Solution | Hypertonic (Severe Plasmolysis) |
Calculation of Tuber Water Potential:
Isotonic sucrose concentration: $M = 0.25text{ M} = 0.25text{ mol/L}$.
Temperature: $t = 22^circtext{C} implies T = 273.15 + 22 = 295.15text{ K}$.
$$Psi_w = -i cdot M cdot R cdot T$$
$$Psi_w = -(1.0) times (0.25text{ mol/L}) times (0.008314text{ MPa}cdottext{L}cdottext{mol}^{-1}cdottext{K}^{-1}) times (295.15text{ K})$$
$$Psi_w = mathbf{-0.613text{ MPa}} quad (text{or } mathbf{-6.13text{ bar}})$$
Physiological Evaluation: A water potential of $-0.613text{ MPa}$ is typical for well-hydrated storage parenchyma tissue in equilibrium with soil moisture under ambient atmospheric conditions.
