KEVOS® MAKEOS · Quality
Polymer Intrinsic Viscosity and Molar Mass from One Viscometer Reading (Single-Point [η], Mark–Houwink)
From the flow times of the solvent and of one dilute polymer solution in a capillary viscometer, what is the intrinsic viscosity, what viscosity-average molar mass does it imply, and is it within my specification?
Dilute-solution viscometry from one concentration: the relative, specific, reduced and inherent viscosities from the flow times, the intrinsic viscosity by the Solomon–Ciuta, Billmeyer or Huggins single-point relation (all three are reported side by side to show their agreement), the viscosity-average molar mass from Mark–Houwink constants you supply, and the intrinsic viscosity against your specification limits, as used for resin grade and degradation checks.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Viscometer readings | ||
| Flow time of the pure solvent | s | Mean flow time of the pure solvent through the capillary viscometer at the bath temperature. |
| Flow time of the polymer solution | s | Mean flow time of the polymer solution in the same viscometer at the same temperature. |
| Polymer concentration of the solution | g/dL | Polymer concentration in grams per decilitre, from the weighed polymer and the solution volume. |
| Method and constants | ||
| Single-point relation for the result | choice | Single-point relation your test method or customer specifies; the other two are shown for comparison. |
| Huggins constant kH | Huggins constant for this polymer and solvent, from a dilution series or the literature; used only by the Huggins relation. | |
| Mark–Houwink constant K | dL/g | Mark–Houwink constant K for this polymer, solvent and temperature, from the literature or a calibration, in dL/g. |
| Mark–Houwink exponent a | Mark–Houwink exponent a for the same polymer, solvent and temperature as K. | |
| Specification | ||
| Lowest acceptable intrinsic viscosity | dL/g | Lowest intrinsic viscosity the grade or specification accepts. |
| Highest acceptable intrinsic viscosity | dL/g | Highest intrinsic viscosity the grade or specification accepts. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
Viscometer readings
What this means: Flow time of the pure solvent
- What it is
- The time the pure solvent takes to flow between the two marks of the capillary viscometer at the bath temperature, the reference for the relative viscosity.
- Units and format
- Enter a number in s: seconds. The form accepts 1 s to 100000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer solvent time lowers the relative viscosity and every result after it.
- Get it right
- Repeat until consecutive times agree closely and use the mean; a dirty capillary shows as a drifting solvent time.
What this means: Flow time of the polymer solution
- What it is
- The time the polymer solution takes to flow between the same marks in the same viscometer and bath; its ratio to the solvent time is the relative viscosity.
- Units and format
- Enter a number in s: seconds. The form accepts 1 s to 100000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 135 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer solution time raises the intrinsic viscosity and the molar mass.
- Get it right
- Filter the solution to remove gel and dust, which lengthen the time.
What this means: Polymer concentration of the solution
- What it is
- The mass of polymer per volume of solution in grams per decilitre, by which every viscosity number is divided to give an intrinsic viscosity in dL/g.
- Units and format
- Enter a number in g/dL: g/dL. The form accepts 0.001 g/dL to 10 g/dL. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 g/dL as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- At the same flow times a higher stated concentration gives a lower intrinsic viscosity.
- Get it right
- 0.5 g/dL is 0.5 g in 100 mL of solution; dry the polymer before weighing it.
Method and constants
What this means: Single-point relation for the result
- What it is
- Which single-point relation converts the one reading into the intrinsic viscosity reported against the specification; all three relations are shown in the table.
- Units and format
- Choose one of 3 options from the list: Solomon–Ciuta; Billmeyer; Huggins, with the Huggins constant below.
- Example
- The form opens with “Solomon–Ciuta” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- Changes the reported intrinsic viscosity by the spread shown between the relations.
- Get it right
- Use the relation named in your test method so results compare with the supplier’s certificate.
What this means: Huggins constant kH
- What it is
- The Huggins constant, the slope of reduced viscosity against concentration divided by the square of the intrinsic viscosity; it is used only by the Huggins relation.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.35 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger Huggins constant lowers the Huggins intrinsic viscosity.
- Get it right
- About 0.3 to 0.4 is common for flexible polymers in good solvents; measure it from a dilution series for your system.
What this means: Mark–Houwink constant K
- What it is
- The Mark–Houwink constant K, the prefactor in [η] = K Mᵃ, specific to the polymer, the solvent and the temperature, in dL/g.
- Units and format
- Enter a number in dL/g: dL/g. The form accepts 1e-7 dL/g to 1 dL/g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0005 dL/g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Mv is proportional to (1 ÷ K) raised to the power 1 ÷ a.
- Get it right
- Constants are often published in mL/g: divide by 100 for dL/g.
What this means: Mark–Houwink exponent a
- What it is
- The Mark–Houwink exponent a, which measures how fast the intrinsic viscosity rises with molar mass and reflects the solvent quality and chain stiffness.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 2. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.7 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller exponent makes the molar mass much more sensitive to the intrinsic viscosity.
- Get it right
- Take K and a as a pair from the same publication; mixing pairs gives a wrong molar mass.
Specification
What this means: Lowest acceptable intrinsic viscosity
- What it is
- The lowest intrinsic viscosity the resin grade or specification accepts.
- Units and format
- Enter a number in dL/g: dL/g. The form accepts 0 dL/g to 20 dL/g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.6 dL/g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the lower line of the specification.
- Get it right
- Compare only results from the same solvent, temperature and single-point relation as the specification.
What this means: Highest acceptable intrinsic viscosity
- What it is
- The highest intrinsic viscosity the resin grade or specification accepts.
- Units and format
- Enter a number in dL/g: dL/g. The form accepts 0.001 dL/g to 20 dL/g. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.75 dL/g as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the upper line of the specification.
- Get it right
- A result above the range can mean a different grade or a concentration error.
Method and formulas
- ηr = t ÷ t₀ (equal densities), ηsp = ηr − 1, reduced viscosity ηsp ÷ c and inherent viscosity ln ηr ÷ c.
- Solomon–Ciuta: [η] = √[2(ηsp − ln ηr)] ÷ c. Billmeyer: [η] = ¼(ηsp + 3 ln ηr) ÷ c. Huggins: ηsp ÷ c = [η] + kH[η]²c solved for [η] = [√(1 + 4kH ηsp) − 1] ÷ (2kH c).
- Mark–Houwink: [η] = K Mᵃ, so Mv = ([η] ÷ K)^(1/a).
- Example: 135.0 s against 100.0 s at 0.5 g/dL: ηr = 1.35, [η] = 0.6318 dL/g (Solomon–Ciuta), 0.6252 (Billmeyer) and 0.6304 (Huggins, kH = 0.35); with K = 5 × 10⁻⁴ dL/g and a = 0.70, Mv = 26,969 g/mol: within 0.60 to 0.75 dL/g.
Limitations
- Single-point relations assume a typical concentration dependence (a Huggins constant near 0.35); for unusual polymers or solvents they drift from the extrapolated value.
- No kinetic-energy or density correction; the solution must be dilute and free of gel or dust.
- Mv depends entirely on the Mark–Houwink constants entered and is not the weight-average molar mass.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check incoming resin against its intrinsic viscosity grade
- Detect molar-mass loss from drying, moulding, extrusion or recycling
- Estimate the viscosity-average molar mass of a polymer
- Compare a single-point result with a full dilution series
Who it is for
- Quality and laboratory staff
- Polymer processing engineers
- Recyclers and resin buyers
What you get
- Relative, specific, reduced and inherent viscosity
- Intrinsic viscosity by the chosen relation and by all three
- Viscosity-average molar mass
- Within or outside the specification
Interpreting the result
- A fall in intrinsic viscosity after processing means chain scission, for example by hydrolysis of an undried resin.
- The exponent a shows solvent quality: about 0.5 in a theta solvent and up to about 0.8 in a good solvent for flexible coils (Klenin chapters 4 and 5).
Before relying on the result
- Repeat each flow time until readings agree, and check the solvent time against the viscometer’s record.
References
- Solomon O. F. and Ciută I. Z., J. Appl. Polym. Sci. 6, 683 (1962): single-point determination of intrinsic viscosity.
- Billmeyer F. W., J. Polym. Sci. 4, 83 (1949): methods for estimating intrinsic viscosity.
- Huggins M. L., J. Am. Chem. Soc. 64, 2716 (1942): concentration dependence of the viscosity of dilute solutions of long-chain molecules.
- Klenin V. J., Thermodynamics of Systems Containing Flexible-Chain Polymers (Elsevier, 1999; ISBN 0-444-82373-5), §5.3 (hydrodynamic properties of macromolecules, intrinsic viscosity of coils) and chapter 4 (scaling of coil size with chain length). Topic reference; no tables are reproduced.
- ISO 1628-1 (viscosity of polymers in dilute solution using capillary viscometers, general principles); ASTM D2857 and, for PET, ASTM D4603. Consult the current editions.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Method explained here · KEVOS® original book
Intrinsic viscosity and resin checks
In Polymer Chains by the Numbers
What it covers: Measure a resin's intrinsic viscosity from viscometer flow times, convert it to a viscosity-average molar mass with Mark–Houwink constants, and use it to check virgin resin, regrind and blends.
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