Polymer Viscosity Measurement Discussion Examples | How to Determine Viscosity-Average Molecular Weight

What Is Polymer Viscosity Measurement?

Polymer viscosity measurement is a method in which the difficulty with which a polymer solution flows is measured, and the molecular weight of the polymer and the state of the molecular chains in solution are evaluated from the results.
In general, when compared at the same concentration, a polymer with a larger molecular weight has a higher solution viscosity.
This is because the polymer chains spread out in solution and interfere with the flow of the solvent.

In experiments, an Ostwald viscometer, Ubbelohde viscometer, or similar instrument may be used to measure the flow times of the solvent and polymer solutions.
Relative viscosity and specific viscosity are determined from the flow times, and intrinsic viscosity is then determined by performing measurements at different concentrations.
Once the intrinsic viscosity is known, the viscosity-average molecular weight can be calculated using the Mark-Houwink equation.

Main Items to Include in the Results

In polymer viscosity measurements, organize the measurement temperature, polymer concentration, solvent flow time, polymer-solution flow time at each concentration, relative viscosity, specific viscosity, reduced viscosity, inherent viscosity, intrinsic viscosity, and viscosity-average molecular weight.
Because viscosity is sensitive to temperature, the measurement temperature must always be recorded.

Main Items to Include in the Results

• Polymer used
• Solvent used
• Measurement temperature
• Viscometer used
• Polymer-solution concentration
• Flow time of the pure solvent
• Flow time of the solution at each concentration
• Relative viscosity
• Specific viscosity
• Reduced viscosity
• Inherent viscosity
• Intrinsic viscosity
• Constants K and a in the Mark-Houwink equation
• Viscosity-average molecular weight
• Graph intercept
• Sources of error and points for improvement

Reference Experimental Values and Molecular-Weight Calculation Examples for Polymer Viscosity Measurement

Here, reference experimental values are organized for determining relative viscosity, specific viscosity, reduced viscosity, and intrinsic viscosity from the flow times obtained in polymer-solution viscosity measurements and for calculating the viscosity-average molecular weight using the Mark-Houwink equation.

In polymer solutions, the polymer chains spread out in the solvent, so the viscosity becomes higher than that of the pure solvent.
By examining the concentration dependence of the solution viscosity, information about the size and molecular weight of the polymer chains can be obtained.

Reference Experimental Conditions

Main Equations Used in Viscosity Calculations

Example Flow-Time Measurements

The following is a reference example in which the solvent flow time is 80.0 seconds and the flow time is measured while varying the concentration of a polystyrene solution.

The flow time becomes longer as the concentration increases.
This is considered to be because the polymer chains interfere with flow in the solvent and increase the viscosity of the solution.

Example Calculation of Relative Viscosity and Specific Viscosity

If the solvent flow time is t0 = 80.0 s and the average flow time of the 0.40 g/dL solution is t = 90.9 s,

Relative viscosity ηr = 90.9 ÷ 80.0 = 1.136

Specific viscosity ηsp = 1.136 − 1 = 0.136

Therefore, the viscosity of the 0.40 g/dL polymer solution can be organized as approximately 13.6% higher than that of the solvent.

Summary of Viscosity Calculation Results

Reduced viscosity and inherent viscosity approach the intrinsic viscosity as the concentration decreases.
In experiments, these values are extrapolated to a concentration of 0 to determine the intrinsic viscosity.

How to Determine Intrinsic Viscosity

Intrinsic viscosity [η] is the extrapolated value of reduced viscosity or inherent viscosity as the concentration approaches 0.
Here, an example is shown in which intrinsic viscosity is determined by linear extrapolation of reduced viscosity.

In this reference example, the intercept obtained by extrapolating the reduced viscosity to a concentration of 0 is taken as [η] = 0.285 dL/g.

If the intercept extrapolated from the inherent viscosity is 0.290 dL/g, the two values are close, and the intrinsic viscosity can be judged to be approximately 0.29 dL/g.

Calculation of Viscosity-Average Molecular Weight Using the Mark-Houwink Equation

The Mark-Houwink equation is used to determine the viscosity-average molecular weight M from the intrinsic viscosity [η].

[η] = K M^a

Under conditions of polystyrene/toluene/25°C, if K = 1.1×10⁻⁴ dL/g, a = 0.73, and the intrinsic viscosity [η] = 0.285 dL/g,

M = ([η] ÷ K)^1/a

M = (0.285 ÷ 1.1×10⁻⁴)^1/0.73 ≒ 4.7×10⁴

Therefore, the viscosity-average molecular weight of this sample is approximately 4.7×10⁴.

Example Comparison of Intrinsic Viscosity and Molecular Weight

Samples with larger intrinsic viscosities have polymer chains that spread more widely in solution and also have larger viscosity-average molecular weights.

Effect of Excessively High Concentration

In viscosity measurements, if the polymer solution is too concentrated, the polymer chains overlap with one another and the solution becomes difficult to treat as a dilute solution.

If high-concentration data are forced into the extrapolation, the intrinsic viscosity may be overestimated and the molecular weight may also be estimated as larger.

Differences in Intrinsic Viscosity Depending on the Solvent

Even for the same polymer, the way the polymer chains expand changes depending on compatibility with the solvent, resulting in changes in intrinsic viscosity.

In a good solvent, polymer chains expand and the intrinsic viscosity becomes larger even for the same molecular weight.
Therefore, the Mark-Houwink constants K and a must be selected for each combination of polymer, solvent, and temperature.

Changes in Flow Time With Temperature

Viscosity is strongly affected by temperature, and as the temperature increases, the viscosity of solvents and solutions often decreases.

Because changes in temperature change the flow time, it is important to use a constant-temperature bath to keep the temperature constant during viscosity measurements.

Comparison of Flow Times for Different Molecular Weights

Even at the same concentration, a polymer with a larger molecular weight has a higher solution viscosity and a longer flow time.

The larger the molecular weight, the longer the polymer chains and the larger the volume they occupy in the solvent, making them more likely to interfere with the flow of the solution.

Example of Variation in Measured Values

Insufficient cleaning of the viscometer, bubbles, temperature fluctuations, and errors in concentration preparation may cause variation in flow times.

If only one flow-time measurement differs greatly, bubbles or a shift in the measurement-start position are suspected.
If all values are high, contamination inside the viscometer or an error in solution concentration is considered.

Example of How to Write the Results

The flow time of the polystyrene solution increased as the concentration increased.
The solvent flow time was 80.0 seconds, while the average flow time of the 0.40 g/dL solution was 90.9 seconds.
From these results, the relative viscosity was 90.9 ÷ 80.0 = 1.136, and the specific viscosity was 1.136 − 1 = 0.136.
Furthermore, the reduced viscosity was calculated as 0.136 ÷ 0.40 = 0.341 dL/g.

When the reduced viscosities obtained at each concentration were extrapolated to a concentration of 0, the intrinsic viscosity was 0.285 dL/g.
The extrapolated value obtained from the inherent viscosity was also 0.290 dL/g, and the two values were close.
This suggests that relatively reasonable extrapolation was possible within the measured concentration range.

Using the Mark-Houwink equation [η] = K M^a, with K = 1.1×10⁻⁴ dL/g and a = 0.73, the viscosity-average molecular weight was calculated to be approximately 4.7×10⁴.
Samples with larger intrinsic viscosities also had larger viscosity-average molecular weights, and their polymer chains are considered to spread more widely in solution.

Points for Connecting the Results to the Discussion

In a discussion of polymer viscosity measurements, rather than simply describing an increase in flow time as “higher viscosity,” it is important to explain it in relation to polymer-chain expansion, molecular weight, solvent, temperature, and concentration range.

• Can relative viscosity be calculated from the flow times of the solvent and solution?
• Can specific viscosity, reduced viscosity, and inherent viscosity be determined from relative viscosity?
• Can intrinsic viscosity be determined by extrapolating reduced viscosity or inherent viscosity to a concentration of 0?
• Can viscosity-average molecular weight be calculated using the Mark-Houwink equation?
• Can the reason why flow time and intrinsic viscosity increase with molecular weight be explained?
• Can it be explained that solvent quality changes the expansion of polymer chains and therefore changes intrinsic viscosity?
• Can deviation of high-concentration data from linearity be explained in relation to overlap of polymer chains?
• Can the effects of temperature fluctuations, bubbles, insufficient viscometer cleaning, and concentration-preparation errors on flow time be discussed?
• Can it be explained that the Mark-Houwink constants differ for each combination of polymer, solvent, and temperature?

Example Discussion

In this experiment, the flow times of dilute polymer solutions were measured and the viscosity-average molecular weight was determined.
In the polystyrene solutions, the flow time increased as the concentration increased.
This is considered to be because the polymer chains in the solution interfered with flow and increased the solution viscosity.
In particular, polymers with larger molecular weights have longer molecular chains and occupy larger volumes in the solvent, resulting in a larger increase in viscosity.

The flow time of the 0.40 g/dL solution was 90.9 seconds compared with a solvent flow time of 80.0 seconds.
From this result, the relative viscosity was 1.136, the specific viscosity was 0.136, and the reduced viscosity was 0.341 dL/g.
When the reduced viscosities obtained at each concentration were extrapolated to a concentration of 0, the intrinsic viscosity was 0.285 dL/g.
Because the extrapolated value obtained from the inherent viscosity was also close, the measurement results were considered generally reasonable.

When the viscosity-average molecular weight was calculated using the Mark-Houwink equation, a value of approximately 4.7×10⁴ was obtained.
This value makes use of the fact that intrinsic viscosity reflects the expansion of polymer chains in solution.
However, the Mark-Houwink constants K and a differ depending on the type of polymer, solvent, and temperature.
Therefore, if constants for a different solvent or temperature are used, the molecular weight may be estimated incorrectly.

On the high-concentration side, the reduced viscosity may deviate from a linear increase.
This is because the polymer chains overlap with one another and can no longer be treated as a dilute solution.
Because intrinsic viscosity is an extrapolated value at a concentration of 0, it is necessary to use highly reproducible data at concentrations as low as possible.

Possible sources of error include temperature fluctuations, bubbles inside the viscometer, errors in solution-concentration preparation, and insufficient cleaning of the viscometer.
Because viscosity is strongly affected by temperature, the measurement temperature must be kept constant using a constant-temperature bath during measurement.
In addition, if bubbles enter the flow path, the flow time may become longer and the viscosity may be overestimated.
Therefore, it is important to thoroughly clean the viscometer before measurement, remove bubbles, and perform multiple measurements.

Summary

In polymer viscosity measurements, relative viscosity, specific viscosity, reduced viscosity, and inherent viscosity are determined from the flow times of the solvent and polymer solutions, and intrinsic viscosity is obtained by extrapolating to a concentration of 0.
Intrinsic viscosity reflects the expansion of polymer chains in solution, and viscosity-average molecular weight can be calculated using the Mark-Houwink equation.

This reference example used polystyrene solutions to address flow-time measurements, viscosity calculations, extrapolation of intrinsic viscosity, viscosity-average molecular weight, concentration dependence, solvent effects, temperature effects, and measurement errors.
In a report, it is useful to show the calculation process and discuss the results in relation to polymer-chain expansion, molecular weight, and measurement conditions.

Why Do Polymer Solutions Have High Viscosity?

Polymers have extremely long molecular chains compared with low-molecular-weight substances.
In solution, polymer chains are not completely extended but often exist in a spread-out, coil-like state.
These expanded molecular chains interfere with the flow of the solvent, increasing the viscosity of the solution.

In addition, as the polymer concentration increases, the molecular chains become closer to one another and entanglement and interactions increase.
Therefore, the higher the concentration, the more difficult the solution becomes to flow.
Viscosity measurements use this concentration dependence to determine intrinsic viscosity.

Relationship Between Flow Time and Viscosity

In experiments using a viscometer, the time required for a fixed amount of liquid to flow through a narrow tube is measured.
When the difference in liquid density is small, the viscosity of the solution can be considered approximately proportional to the flow time.
Therefore, relative viscosity can be determined by comparing the flow times of the pure solvent and polymer solution.

Strictly speaking, however, viscosity is also related to density.
Some laboratory manuals omit density correction, but when the concentration is high or the density difference cannot be ignored, the effect of density must also be considered.

What Is Relative Viscosity?

Relative viscosity is a value representing how many times greater the viscosity of a polymer solution is than that of the pure solvent.
When measured with a viscometer under conditions where the density difference can be ignored, it is determined by dividing the solution flow time by the solvent flow time.

Relative viscosity ηr = Solution flow time t ÷ Solvent flow time t0

Relative viscosity indicates how much more difficult the solution becomes to flow when polymer is added.
If the relative viscosity is greater than 1, the polymer solution has a higher viscosity than the pure solvent.

What Is Specific Viscosity?

Specific viscosity is a value representing how much the viscosity increased because of the addition of polymer.
It is determined by subtracting 1 from the relative viscosity.
In other words, it represents the increase in viscosity relative to the pure solvent.

Specific viscosity ηsp = ηr − 1

The larger the specific viscosity, the greater the increase in viscosity caused by the polymer.
Specific viscosity is a basic value used to determine reduced viscosity and intrinsic viscosity.

What Is Reduced Viscosity?

Reduced viscosity is the specific viscosity divided by the polymer concentration.
It represents how much the viscosity increases per unit concentration of polymer.
Reduced viscosity may be plotted against concentration to determine intrinsic viscosity.

Reduced viscosity = ηsp ÷ c

In a sufficiently low-concentration region, the value obtained by extrapolating the reduced viscosity to a concentration of 0 is the intrinsic viscosity.
This extrapolation allows the viscosity effect to be evaluated in an infinitely dilute state in which interactions among polymer chains are almost absent.

What Is Inherent Viscosity?

Inherent viscosity is the natural logarithm of relative viscosity divided by concentration.
Like reduced viscosity, it is used to determine intrinsic viscosity by extrapolation to a concentration of 0.
In some experiments, both reduced viscosity and inherent viscosity are plotted, and intrinsic viscosity is determined as their common intercept.

Inherent viscosity = ln(ηr) ÷ c

Ideally, the extrapolated values of reduced viscosity and inherent viscosity approach the same intrinsic viscosity.
If the difference between the two is large, possible causes include an excessively high concentration range, large measurement errors, or a solution that is not sufficiently dilute.

What Is Intrinsic Viscosity?

Intrinsic viscosity is a value representing the increase in viscosity per unit concentration of polymer as the concentration approaches infinitely close to 0.
It indicates how much a single polymer molecule affects solution viscosity under conditions where interactions among polymer chains are almost absent.
Intrinsic viscosity is related to the molecular weight of the polymer and its expansion in solution.

[η] = lim_c→0 (ηsp / c)

A larger intrinsic viscosity may indicate that the polymer chains spread more widely in solution or that the molecular weight is larger.
However, intrinsic viscosity is affected not only by molecular weight but also by compatibility with the solvent, temperature, chain rigidity, and branching.

How to Determine Intrinsic Viscosity

To determine intrinsic viscosity, the flow times of polymer solutions at multiple concentrations are measured, and relative viscosity, specific viscosity, and reduced viscosity are calculated.
The reduced viscosity is then plotted against concentration, and the straight line is extrapolated to a concentration of 0.
This intercept is the intrinsic viscosity.

In some experiments, inherent viscosity is also plotted against concentration, and the intrinsic viscosity is determined as the common intercept of the extrapolated reduced-viscosity and inherent-viscosity lines.
If the concentration range is appropriate, the two lines show similar intercepts.

What Is the Mark-Houwink Equation?

There is an empirical relationship between intrinsic viscosity and polymer molecular weight.
This is called the Mark-Houwink equation.
Using this equation, the viscosity-average molecular weight can be determined from intrinsic viscosity.

[η] = K M^a

Here, [η] is the intrinsic viscosity, M is the viscosity-average molecular weight, and K and a are constants determined by the polymer, solvent, and temperature.
Therefore, K and a are not common values for all polymers, and values corresponding to the experimental conditions must be used.

How to Determine Viscosity-Average Molecular Weight

Viscosity-average molecular weight is determined by substituting the intrinsic viscosity into the Mark-Houwink equation.
Rearranging the Mark-Houwink equation gives the following expression.

M = ([η] / K)^1/a

First, the intrinsic viscosity [η] is determined from viscosity measurements.
Next, K and a given in the laboratory manual or literature are used and substituted into the equation above.
Care is required because if the unit of intrinsic viscosity does not correspond to the unit of K, the molecular weight will be calculated incorrectly.

Meaning of Viscosity-Average Molecular Weight

Because polymers have molecular-weight distributions, there are several types of average molecular weight.
Representative examples include number-average molecular weight Mn, weight-average molecular weight Mw, and viscosity-average molecular weight Mv.
Viscosity-average molecular weight is an average molecular weight determined from viscosity measurements and reflects the hydrodynamic size of the molecular chains.

Mv is not exactly the same value as Mn or Mw.
For samples with a molecular-weight distribution, the average molecular weight obtained differs depending on the measurement method.
Therefore, values obtained by GPC or light scattering may not agree with values obtained by the viscosity method.

Relationship Between Concentration and Viscosity

As the concentration of a polymer solution increases, the viscosity generally increases.
This is because the number of polymer chains in the solution increases and interactions and entanglement among the molecular chains increase.
Particularly at high concentrations, the solution becomes difficult to treat as a dilute solution, and linear extrapolation may become difficult.

To determine intrinsic viscosity, it is important to perform measurements over as dilute a concentration range as possible.
If the concentration is too high, interactions among polymer chains become strong, making errors more likely when extrapolating to infinite dilution.

Effect of Temperature on Viscosity

Viscosity is extremely sensitive to temperature.
In general, as the temperature increases, solvents and solutions become easier to flow and their viscosity decreases.
Therefore, it is important to use a constant-temperature bath to keep the measurement temperature constant during viscosity measurements.

If the temperature is not constant, the flow time changes even for the same sample, causing errors in relative viscosity and intrinsic viscosity.
Because viscosity-average molecular weight is determined from intrinsic viscosity, errors in temperature control also affect the final molecular weight.

Effect of the Solvent

Intrinsic viscosity is affected by compatibility between the polymer and solvent.
In a good solvent, polymer chains interact well with the solvent and tend to take on an expanded conformation.
As a result, the intrinsic viscosity tends to become larger.
In contrast, in a poor solvent, polymer chains tend to contract and the intrinsic viscosity may become smaller.

In other words, even for a polymer of the same molecular weight, the intrinsic viscosity changes when the solvent changes.
This is also why the K and a values in the Mark-Houwink equation differ depending on the solvent.

Effect of Branching Structure

The branching structure of a polymer also affects viscosity.
When compared at the same molecular weight, linear polymers tend to spread more widely in solution and have a larger effect on viscosity.
In contrast, branched polymers may adopt a relatively compact conformation even at the same molecular weight and may therefore have a smaller intrinsic viscosity.

Therefore, when determining viscosity-average molecular weight, it is important that the Mark-Houwink constants correspond to the structure of the polymer being measured.
If constants for a linear polymer are used for a branched polymer, the estimated molecular weight may be shifted.

Reasons the Viscosity-Average Molecular Weight May Differ From the Expected Value

If the viscosity-average molecular weight is smaller than expected, possible causes include insufficient polymerization, low molecular weight, polymer degradation, an incorrect solution concentration, or errors in extrapolation of intrinsic viscosity.
Conversely, if the value is larger than expected, possible causes include concentration-calculation errors, aggregation in the solution, insufficient filtration, contamination by insoluble matter, and errors in reading flow time.

The viscosity method is simple, but it does not measure molecular weight directly.
Because it estimates molecular weight through intrinsic viscosity, the measurement conditions and selection of constants have a large effect on the result.

Errors in Flow-Time Measurement

In viscosity measurements, accurate reading of the flow time is important.
Delays in operating the stopwatch, differences in the position at which the liquid level is read, bubbles, contamination of the viscometer walls, and temperature changes cause errors in the flow time.
Errors in flow time affect relative viscosity, specific viscosity, reduced viscosity, intrinsic viscosity, and viscosity-average molecular weight.

Particularly when the difference in flow time between the solvent and a low-concentration solution is small, even a slight reading error produces a large relative error.
It is important to perform multiple measurements and use the average value.

Errors Caused by Bubbles

If bubbles enter the viscometer, they disturb the liquid flow or change the actual volume of liquid flowing through the instrument.
As a result, the flow time becomes unstable and the measured values vary.
Because polymer solutions have high viscosity, bubbles may be difficult to remove.

To prevent bubbles, it is important to introduce the solution gently into the viscometer, confirm that no bubbles are present before measurement, and perform filtration or degassing when necessary.
Data measured while bubbles are present are less reliable.

Errors in Solution Concentration

In viscosity measurements, the polymer-solution concentration is directly involved in the calculations.
Errors in polymer weighing, insufficient drying, errors in measuring solvent volume, and errors in dilution operations cause the concentration to shift.
If the concentration is incorrect, the reduced viscosity and inherent viscosity change, which also affects the extrapolation of intrinsic viscosity.

In addition, if the polymer is not completely dissolved, the actual polymer concentration in the solution becomes lower than the calculated value.
Insufficient dissolution and contamination by insoluble matter are also important sources of error in viscosity measurements.

Errors Caused by Insufficient Dissolution

Polymers may require a long time to dissolve.
If measurements are performed before dissolution is complete, insoluble matter or aggregates remain in the solution and make the flow time unstable.
In addition, because the amount of polymer actually dissolved is smaller than the calculated value, errors also occur in calculations based on concentration.

If insoluble matter or aggregates affect the capillary of the viscometer, the flow may be obstructed and an abnormally long flow time may result.
It is important to dissolve the polymer sufficiently before measurement and filter the solution when necessary.

Errors Caused by Insufficient Cleaning of the Viscometer

If previous samples or contamination remain on the inner walls of the viscometer, the liquid flow changes and causes errors in the flow time.
Because polymer solutions have high viscosity and readily remain inside the viscometer, cleaning between measurements is important.
Insufficient cleaning has a particularly large effect when low-concentration samples are measured.

In addition, if solvent or water remains after cleaning, the next solution introduced may be diluted.
After cleaning, the viscometer must be dried appropriately or rinsed with the measurement solvent.

Discussion When the Graph Is Not Linear

When reduced viscosity or inherent viscosity is plotted against concentration, a linear relationship is ideally obtained in the low-concentration region.
However, the points may deviate from a straight line if the concentration is too high, measurement errors are large, the polymer is aggregated, the solution is nonuniform, or the temperature is not constant.

If the graph is not linear, rather than forcing all points into a linear approximation, the concentration range and the cause of outliers should be discussed.
Particularly when deviation occurs on the high-concentration side, interactions and entanglement among polymer chains may be involved.

When Viscosity-Measurement Results Can Be Considered Good

Results can be considered good when the flow time and relative viscosity increase reasonably as the concentration increases, the reduced-viscosity and inherent-viscosity plots are approximately linear in the low-concentration region, and a reasonable intrinsic viscosity is obtained by extrapolation.
It is also important that the variation in flow time be small when the same sample is measured multiple times.

Furthermore, if the obtained viscosity-average molecular weight does not greatly contradict literature or expected values, it becomes easier to judge that the measurement conditions and calculations were generally appropriate.
However, because the viscosity method is based on an empirical equation, complete agreement should not be expected, and differences in conditions must be considered.

Example Discussion When the Experiment Did Not Go Well

If a viscosity measurement does not go well, possible causes are considered from results such as large variation in flow time, an unnatural relationship between concentration and viscosity, a nonlinear graph, a negative intrinsic viscosity, or an extremely large or small molecular weight.
Organizing the possible causes separately into temperature, concentration, dissolution state, bubbles, viscometer contamination, and flow-time reading makes the discussion easier.

How to Write Points for Improvement

In a discussion of polymer viscosity measurements, including not only sources of error but also points for improvement makes the report easier to organize.
Improvements can be divided into solution preparation, temperature control, viscometer operation, time measurement, and graph preparation.

Improvements to Solution Preparation

• Weigh the polymer accurately
• Dry the polymer sufficiently before weighing
• Measure the amount of solvent accurately
• Dissolve the polymer completely
• Filter the solution to remove insoluble matter when necessary
• Perform dilution accurately

Improvements to Measurement Operation

• Keep the measurement temperature constant using a constant-temperature bath
• Clean the viscometer thoroughly
• Rinse the viscometer with the measurement solvent
• Prevent bubbles from entering
• Accurately read the moment when the liquid level passes the mark
• Perform multiple measurements and use the average value

Improvements to Analysis

• Perform measurements in the low-concentration region
• Investigate the causes of outliers
• Check both reduced viscosity and inherent viscosity
• Carefully extrapolate to a concentration of 0
• Check the units of the Mark-Houwink constants
• Use K and a corresponding to the polymer, solvent, and temperature

Difference Between a Superficial Discussion and a Good Discussion

In a discussion of polymer viscosity measurements, simply writing that “the flow time was longer at higher concentrations” or “the molecular weight was determined” results in a superficial discussion.
Relating flow time, relative viscosity, specific viscosity, intrinsic viscosity, the Mark-Houwink equation, and measurement errors produces a more persuasive discussion.

Examples of Expressions That Can Be Used in Reports

The following expressions can be used when writing the results and discussion of polymer viscosity measurements.
Adjust the necessary parts according to your own experimental results.

• Because the flow time of the polymer solution was longer than that of the pure solvent, the solution viscosity is considered to have increased.
• Polymer chains spread out in solution and interfere with solvent flow, thereby increasing viscosity.
• Relative viscosity indicates how many times greater the viscosity of the polymer solution is than that of the pure solvent.
• Specific viscosity represents the increase in viscosity caused by the addition of polymer.
• Intrinsic viscosity can be determined by extrapolating reduced viscosity to a concentration of 0.
• Intrinsic viscosity represents the contribution of the polymer to viscosity in the infinitely dilute state.
• The Mark-Houwink equation can be used to determine viscosity-average molecular weight from intrinsic viscosity.
• Viscosity-average molecular weight is an average molecular weight different from number-average molecular weight and weight-average molecular weight.
• Because viscosity is sensitive to temperature, the measurement temperature must be kept constant.
• Solution concentration, dissolution state, bubbles, and contamination of the viscometer affect the flow time and molecular-weight calculation.

Points to Check in Polymer Viscosity Measurements

Checking the following points before writing the report makes the discussion easier to write.

• Have the flow times of the pure solvent and polymer solutions been organized?
• Are the meanings of relative viscosity, specific viscosity, and reduced viscosity distinguished?
• Has intrinsic viscosity been determined by extrapolation to a concentration of 0?
• Have the reduced-viscosity and inherent-viscosity graphs been checked?
• Has the Mark-Houwink equation been used correctly?
• Has it been confirmed that K and a correspond to the polymer, solvent, and temperature?
• Has the relationship between intrinsic viscosity and molecular weight been explained?
• Has the meaning of viscosity-average molecular weight been explained?
• Has the importance of temperature control been described?
• Have errors in solution concentration been considered?
• Have the effects of insufficient polymer dissolution and bubbles been discussed?
• Do the points for improvement correspond to the sources of error?

Summary

In polymer viscosity measurements, the flow times of the pure solvent and polymer solutions are compared to determine relative viscosity, specific viscosity, reduced viscosity, and intrinsic viscosity.
Polymer chains spread out in solution and interfere with solvent flow, so the viscosity of a polymer solution becomes higher than that of the pure solvent.
As the concentration increases, the flow time and viscosity generally increase.

Intrinsic viscosity is determined by extrapolating reduced viscosity or inherent viscosity to a concentration of 0 and represents the contribution of the polymer to viscosity in the infinitely dilute state.
By substituting this intrinsic viscosity into the Mark-Houwink equation, the viscosity-average molecular weight can be determined.
However, because K and a differ depending on the polymer, solvent, and temperature, constants corresponding to the experimental conditions must be used.

In a report, rather than simply writing that “the flow time was long,” organize the meanings of relative viscosity, specific viscosity, intrinsic viscosity, and viscosity-average molecular weight, and discuss sources of error such as temperature, concentration, insufficient dissolution, bubbles, and contamination of the viscometer.
Viscosity measurement is a simple method for estimating molecular weight, but it is important to recognize that the measurement conditions and analysis method greatly affect the results.