FCSXpert Solutions: Fluorescence Correlation Spectroscopy Simplified!.
## FCS Classroom

#### Autocorrelation Example: Viscosity Titration

### Theoretical Backgroundback to top

#### Physical Properties that Determine τ_{D}

#### Rhodamine 6G Properties

### Experimental Methodback to top

#### Sample Preparation

#### Measurement Conditions

### Resultsback to top

The QuantumXpert provides an ideal method of measuring solvent viscosities in volumes as low as 25µL.

In this experiment, solvent viscosities from 1.15 – 20 cP were used to simulate diffusion measurements of protein-sized particles from 2,000 – 10,000,000 Daltons.
The relationship between correlation time (τ_{D}) and viscosity was found to be linear over the entire experimental range.

See the following sections for detailed information:

The QuantumXpert provides a measure of the size of particles in a given sample by calculating the correlation time, τ_{D},
which is determined by the diffusion coefficient, D, of the fluorescent particles in a sample according to the following equation:

where ω is the instrument’s beam radius.

The diffusion coefficient of a particle is in turn determined by two properties: the viscosity of the solvent, η, and the hydrodynamic radius of the particle, R_{h}.
This relationship is described by the Einstein equation below:

where k_{B} is the Boltzmann constant (1.38x10^{-23} J/K), T is the temperature, and the particle is assumed to be spherical.

This relationship means that increasing the solvent viscosity two-fold has the same effect on D, and therefore on τ_{D},
as increasing the particle radius two-fold.

From the well-determined diffusion coefficient of Rhodamine 6G in water, 2.8x10^{-6} cm^{2}/sec (η = 1.0 cP at 20°C),
we can calculate that R_{h}(R6G) = 7.7x10^{-10} m.

Solutions of glycerol in water were made at 10 different weight percents shown in Table 1. Rhodamine 6G was then added to a concentration of 1.5nM. The viscosities of these solutions (shown in Table 1) were then measured with a Brookfield DV II+ viscometer.

The fluorescence correlation functions were measured with a QuantumXpert spectrometer at a laser attenuation of 1.5 OD and measurement time of 60 seconds.

**Table 1.** Sample viscosities.

Glycerol % (w/w) | Viscosity (cP) |
---|---|

0 | 1.15 |

20 | 2.00 |

30 | 2.65 |

40 | 3.70 |

45 | 4.80 |

50 | 5.65 |

55 | 7.65 |

60 | 9.85 |

65 | 13.7 |

70 | 20.0 |

Table 2, below, lists the calculated values of D and effective particle radius (if viscosity were constant at η = 1).
The fitted values of τ_{D} are also listed with the standard error and sample size.

**Table 2.** Effective radii and correlation times at varying viscosities.

Viscosity (cP) | D (cm^{2}/sec)
| R_{h} (m)
| τ_{D}
| Std Error (N) |
---|---|---|---|---|

1.15 | 2.4x10^{-6} |
8.9x10^{-10} |
0.00155 | 5.26x10^{-5} (10) |

2.00 | 1.4x10^{-6} |
1.5x10^{-9} |
0.00276 | 1.73x10^{-4} (10) |

2.65 | 1.1x10^{-6} |
2.0x10^{-9} |
0.00400 | 1.66x10^{-4} (10) |

3.70 | 7.6x10^{-7} |
2.8x10^{-9} |
0.00642 | 4.97x10^{-4} (9) |

4.80 | 5.8x10^{-7} |
3.7x10^{-9} |
0.00672 | 3.49x10^{-4} (8) |

5.65 | 5.0x10^{-7} |
4.4x10^{-9} |
0.00863 | 3.29x10^{-4} (10) |

7.65 | 3.6x10^{-7} |
5.9x10^{-9} |
0.0114 | 8.71x10^{-4} (10) |

9.85 | 2.8x10^{-7} |
7.6x10^{-9} |
0.0127 | 8.74x10^{-4} (6) |

13.7 | 2.0x10^{-7} |
1.1x10^{-8} |
0.0223 | 0.00192 (5) |

20.0 | 1.4x10^{-7} |
1.5x10^{-8} |
0.0281 | 0.0015 (10) |

The plot of τ_{D} vs. viscosity (Figure 1) shows that the relationship between τ_{D} and viscosity is linear over the entire experimental range.

The effective particle radii range from R_{h} = 8.8x10^{-10} – 1.5x10^{-8} m.
For proteins, this corresponds to a molecular weight range of approximately 2,000 – 10,000,000 Daltons (assuming spherical particles with density of 1.2 g/cm^{3}).