## Susan C. Ross |

Director, Center for Science and Mathematics Education; PI responsible for administration of the grant and for the science education component.

1994: Ph.D., University of Georgia, Mathematics Education, with Patricia Wilson

1989: MSE, Mississippi State University, Mathematics Education

1986: BSE, Delta State University, Mathematics Education

1981: AA, Holmes Community College, Secondary Education

1998 - present: | Director, Center for Science and Mathematics Education, USM |

1994 - 1998: | Assistant Professor of Mathematics, USM |

1993 - 1994: | Instructor in Mathematics Department, Berry College |

1989 - 1993: | Graduate Assistant, The University of Georgia |

1986 - 1989: | Mathematics teacher, Itawamba County Schools |

National Council of Teachers of Mathematics, National Supervisors of Mathematics, Mathematical Association of America, Mississippi Council of Teachers of Mathematics, Mississippi Teachers of College Mathematics, Mississippi Science Teachers Association

Ross, S. C., & Pratt- Cotter. (Summer 1997). Subtraction in the United States: An Historical Perspective, The Mathematics Educator, vol. 8(1).

Ross, S. C., & Hebert, D. (December 1998). A quandary with quadrilateral definitions. Mathematics Teacher, vol. 91(9).

An Alternative Algorithm for Work Problems. Accepted by The Mathematics Educator but not yet published. Co-Author, Sandra Abatemarco,

Ross, S. C., & Pratt-Cotter, M. (November 1999). Subtraction From an Historical Perspective, School Science and Mathematics, vol. 99(7).

Present:

Scholar for The National Faculty, Reviewer for Key Curriculum Press, Reviewer for the Journal of Mathematics Teacher Education, President of Mississippi Council of Teachers of Mathematics, Secretary of Mississippi Teachers of College Mathematics, Conference Chair for 2002 South Regional Conference for the National Council of Teachers of Mathematics, Member of the Professional Education Committee (PEC) and the Executive Committee for the PEC at USM

Reviewer Journal of Research in Mathematics Education, Consultant for Geometry Forum, Assistant Editor of The Mathematics Educator, Presenter at 2 International, 5 National, 10 regional, 40 state/local conferences

Lida McDowell, Burnette Hamil, Mary Pratt-Cotter, Sammy Parker, Rudy Sirochman, David Hebert, Dianne Lewis, William McHenry, Janine Scott

Deborah Booth, Margaret West

Susan Nodurft, Deanna Noyles, Melinda Gann, Martha Goss, Georgia Miller, Melinda Gann, David Hebert

The Center for Science and Mathematics Education does not have an undergraduate program. I do not currently have any undergraduate student Advisees.

As a faculty member in the mathematics department, I advised approximately 25 students per year. Over the last five years, I have advised approximately 100 undergraduate students. All were secondary mathematics education majors. Selected students are: Susan Charles, Thomas Hartfield, Mary Basinger, Tara Ladner, Karen Bond, Jacqueline Woods, Keisha Smith.

None.

Four Ph.D. dissertations.

SCR is currently serving as principal investigator for a Title II Eisenhower Education Grant titled Mathematics and Science Partnership for Implementing National Standards (MSPINS). This grant involves working with four schools districts in developing leadership teams that is involved in writing a district plan for implementing national standards in either science or mathematics. SCR is also currently serving as a Co-PI for a U.S. Dept. of Ed. Grant titled Preparing Teachers to Teach with Technology (PT3). USM is a subcontract with Mississippi State University, the recipients of the grant. SCR is coordinating the USM subcontract. Focusing on the undergraduate course in science and mathematics specifically designed for elementary majors, this project focuses on integrating the use of technology into the teaching of science and mathematics on the elementary level. In the past, SCR has served as principal investigator or project director on six grants, all of which focused on improving the teaching of mathematics and/or science for grade levels K-12.

SCR has always focused on the connection between mathematics content knowledge and mathematics education. Research interests has focused on an exploration of the conceptual understanding elementary preservice teachers have of mathematics, to the history of mathematics and mathematics education, to the integration of technology into K-12 mathematics and science curriculum. low this conversion. Another reason for measuring the polymerization rate at low conversions is that during the early stages of the reaction, the initiator and monomer concentrations remain relatively constant, and you don't have to worry about measuring changes in these values.

Molecular weight can be moderated through the addition of chain transfer agents such as an alkylmercaptan. One which is widely used is dodecyl mercaptan. This molecule readily transfers a hydrogen from the sulfur to a carbon radical:

The various relations of the rate constantskand how they affect the rate of polymerization can be summarized as:_{tr}, k_{i}, and k_{p}There is a characteristic chain transfer constant (C

1.k_{p}>> k_{tr}andk_{i}` ~ k_{p}no change in R_{p}2.k_{p}>> k_{tr}andk_{i}` < k_{p}decrease in R_{p}3.k_{p}<< k_{tr}andk_{i}` < k_{p}large decrease in R_{p}4.k_{p}<< k_{tr}andk_{i}` ~ k_{p}no change in R_{p}5.k_{p}>> k_{tr}andk_{i}` > k_{p}no change in R_{p}6.k_{p}<< k_{tr}andk_{i}` > k_{p}no change in R_{p}_{tr}) for each chain transfer agent - monomer system defined as:

In this experiment the rate of polymerization will be measured by the use of dilatometry. Dilatometry utilizes the volume change that occurs upon polymerization to follow conversion versus time. The conversion is conveniently followed in a dilitometer whose volume includes a capillary region. The dilatometer is placed in a constant temperature bath and the volume change of the polymerizing system, which is quantitatively related to the percent conversion, is followed with time. Dilatometry is not useful for most step polymerizations where there is a small molecule by-product that results in no appreciable volume change upon polymerization.

As the dilatometer is placed into the constant temperature bath, initial meniscus movement is due to two factors:

1. thermal expansion of the styrene monomerAfter approximately 5-10 minutes the effects due to thermal expansion become negligible. If the capillary cross-section area is determined, usually in terms of volume as a function of length, the change in height of monomer in the capillary may be expressed as a volume change. Thus the slope of a plot of meniscus height versus time would give us DH/Dt, which can easily be converted to a volume to give DV/Dt. Some dilatometers have the capillary calibrated in volume increments, thus DV/Dt is directly accessible.2. contraction due to polymerization.

The total fractional change in volume corresponds to complete conversion to polymer of density d

_{2}from W_{1}grams of monomer of density d_{1}. The weight of the polymer would also be W_{1}, since in an addition polymerization, no weight is gained or lost. For the total fractional change in volume, this gives:

which simplifies to:

The degree of monomer conversion would then be:

where D[M] is the incremental change in monomer concentration [M] and DV is the change in volume from the initial volume V

_{o}. This is true, since the term (d_{2}-d_{1})/d_{2}is the fractional volume change which would occur at 100% conversion and DV/V_{o}is the fractional volume change at any time Dt. The ratio of these two quantities should give the fraction of conversion. Note that the quantity is dimensionless, so that D[M] and [M] could be in units of grams, moles, or molar quantities since the units cancel out. Now if both sides of Equation 17 are divided by Dt, incremental time, and rearranged, then

and

The value -d[M]/dt has been previously defined as the overall rate of polymerization, R

_{p}. Equation 13 can be tested by varying the initiator concentration. Additionally, this experiment will test the effect of a chain transfer agent, dodecyl mercaptan, on the rate of the polymerization.

1. Clean and dry the dilatometer. Concentrated nitric acid works well for cleaning out any residues . Then rinse with DI water first, acetone second and then dry with nitrogen.2. Load the dilatometer with the mixture you made for Free-Radical Polymerization (

NOTE: The volume of the dilatometer is approximately 10 ml), Use a rubber pipette bulb to bring the polymerization mixture into the capillary tube so that the liquid level is equal to the lowest graduation. There should be no bubbles anywhere from the bottom of the stopcock to the liquid level in the capillary. While the level is being held in the capillary, the stopcock is closed so that the only opening is at the top of the capillary.(NOTE: Total volume of precision bore capillary is 1.400 ml ± 0.015 ml. The smallest graduation is 0.005 ml.)3. The dilatometer is clamped in a constant temperature bath at 70

^{o}C. Timing is started as soon as the dilatometer is placed in the bath. Initial meniscus movement is due to two factors: Thermal expansion of the liquid and contraction due to polymerization. The liquid level is monitored as a function of time approximately every 2-3 minutes until the level is outside of the calibration marks or for 30-40 minutes.4. The polymerization mixture is emptied from the dilatometer. If the mixture is allowed to remain in the apparatus too long, it will be impossible to remove. The dilatometer is cleaned, as in step 1.

5. The dilatometer is now

cleaned, dried, and stored

1. Prepare a table listing time (t) and a measure of capillary volume, either direct volume (V) or liquid height in the capillary (H) for each run.2. Make a graph of either V vs t or H vs t, depending on which quantity was measured, and take the slope of the straight portion of the line. If the graph is V vs t, the slope will be DV/Dt. If the graph is of DH/Dt, this quantity can be changed to DV/Dt by the use of the calibration constant in ml/cm.

3. Using Equation A we can determine 3. D[M]/ Dt since we have DV/Dt from the previous step. d1 and d2 are the densities of styrene and polystyrene respectively (0.860 and 1.046 g/m; respectively at 70oC), and the term [M]/Vo can be calculated where Vo is the original volume (bulb + capillary) and [M] is the molar concentration of styrene. If we assume that the amount of DDM does not affect the concentration of styrene in bulk styrene, we can use the density (0.860 g/ml) and the to get the concentration in mol/l .

4. The overall rate of polymerization should be calculated for all three samples so that the effect of initiator concentration of the rate may be verified (samples 1 and 2) and also the effect of a chain transfer agent on the rate may be investigated (samples 1 and 3).

1. Pearce, Eli M., Carl E. Wright, Binoy K. Bordoloi.Laboratory Experiments in Polymer Synthesis and Characterization. Educational Modules for Materials Science and Engineering Project, 1982.2. Odian, G.

Principles of Polymerization2nd Edition, Wiley-Interscience, New York, pp. 192-193.## Pre-lab Quiz

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