Applications of generating functions to polymerization kinetics. 3. General procedure illustrated for propagation with monomer conversion

1993 ◽  
Vol 14 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Kevin W. McLaughlin ◽  
Craig M. Bertolucci
Keyword(s):  
Generating Functions ◽  
General Procedure ◽  
Monomer Conversion ◽  
Polymerization Kinetics

Generalizations of the elementary renewal theorem to distributions defined by concave recurrence relations

1977 ◽  
Vol 14 (3) ◽  
pp. 516-526
Author(s):  
W. Reh
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Probability Distributions ◽  
Branching Processes ◽  
General Procedure ◽  
Renewal Function ◽  
Renewal Theorem ◽  
Probability Generating Functions ◽  
Dependent Probability

The paper examines the renewal function associated with a sequence of probability distributions, which is defined by concave recurrence relations or by an even more general procedure. The elementary renewal theorem is generalized to such sequences. The results can be used to establish renewal theorems for first death in branching processes, if only the possibly generation dependent probability generating functions converge to a limit.

scholarly journals Polymerization Kinetics Stability, Volumetric Changes, Apatite Precipitation, Strontium Release and Fatigue of Novel Bone Composites for Vertebroplasty

2018 ◽  
Author(s):  
Piyaphong Panpisut ◽  
Kirsty Main ◽  
Muhammad Adnan Khan ◽  
Mayda Arshad ◽  
Wendy Xia ◽  
...  
Keyword(s):  
Heat Generation ◽  
Glass Fibers ◽  
Monomer Conversion ◽  
Reaction Rates ◽  
Polymerization Kinetics ◽  
Fatigue Properties ◽  
Apatite Formation ◽  
Maximum Reaction ◽  
Urethane Dimethacrylate ◽  
Lower Temperature

AbstractPurposeThe aim was to determine effects of diluent monomer and monocalcium phosphate monohydrate (MCPM) on polymerization kinetics and volumetric stability, apatite precipitation, strontium release and fatigue of novel dual-paste composites for vertebroplasty.Materials and methodsPolypropylene (PPGDMA) or triethylene (TEGDMA) glycol dimethacrylates (25 wt%) diluents were combined with urethane dimethacrylate (70 wt%) and hydroxyethyl methacrylate (5 wt%). 70 wt% filler containing glass particles, glass fibers (20 wt%) and polylysine (5 wt%) was added. Benzoyl peroxide and MCPM (10 or 20 wt%) or N-tolyglycine glycidyl methacrylate and tristrontium phosphate (15 wt%) were included to give initiator or activator pastes. Commercial PMMA (Simplex) and bone composite (Cortoss) were used for comparison.ATR-FTIR was used to determine thermal activated polymerization kinetics of initiator pastes at 50-80 °C. Paste stability, following storage at 4-37 °C, was assessed visually or through mixed paste polymerization kinetics at 25 °C. Polymerization shrinkage and heat generation were calculated from final monomer conversions. Subsequent expansion and surface apatite precipitation in simulated body fluid (SBF) were assessed gravimetrically and via SEM. Strontium release into water was assessed using ICP-MS. Biaxial flexural strength (BFS) and fatigue properties were determined at 37 °C after 4 weeks in SBF.ResultsPolymerization profiles all exhibited an inhibition time before polymerization as predicted by free radical polymerization mechanisms. Initiator paste inhibition times and maximum reaction rates were described well by Arrhenius plots. Plot extrapolation, however, underestimated lower temperature paste stability. Replacement of TEGDMA by PPGDMA, enhanced paste stability, final monomer conversion, water-sorption induced expansion and strontium release but reduced polymerisation shrinkage and heat generation. Increasing MCPM level enhanced volume expansion, surface apatite precipitation and strontium release. Although the experimental composite flexural strengths were lower compared to those of commercially available Simplex, the extrapolated low load fatigue lives of all materials were comparable.ConclusionsIncreased inhibition times at high temperature give longer predicted shelf-life whilst stability of mixed paste inhibition times is important for consistent clinical application. Increased volumetric stability, strontium release and apatite formation should encourage bone integration. Replacing TEGDMA by PPGDMA and increasing MCPM could therefore increase suitability of the above novel bone composites for vertebroplasty. Long fatigue lives of the composites may also ensure long-term durability of the materials.

l-Lactide polymerization studied by 1H NMR with diffusion-ordered spectroscopy (DOSY): a “One NMR Tube Experiment” providing data on monomer conversion, polymer structure, Mn and Mw

2015 ◽  
Vol 6 (24) ◽  
pp. 4353-4357 ◽  
Author(s):  
P. Lewinski ◽  
S. Sosnowski ◽  
S. Kazmierski ◽  
S. Penczek
Keyword(s):  
1H Nmr ◽  
Molar Mass ◽  
Monomer Conversion ◽  
Polymer Structure ◽  
Polymerization Kinetics ◽  
Average Molar Mass ◽  
On Line ◽  
First Time ◽  
Lactide Polymerization

The standard NMR and DOSY techniques allowed for the first time the on-line study of the polymerization kinetics together with the determination of number average molar mass Mn and mass average molar mass Mw.

Generalizations of the elementary renewal theorem to distributions defined by concave recurrence relations

1977 ◽  
Vol 14 (03) ◽  
pp. 516-526
Author(s):  
W. Reh
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Probability Distributions ◽  
Branching Processes ◽  
General Procedure ◽  
Renewal Function ◽  
Renewal Theorem ◽  
Probability Generating Functions ◽  
Dependent Probability

The paper examines the renewal function associated with a sequence of probability distributions, which is defined by concave recurrence relations or by an even more general procedure. The elementary renewal theorem is generalized to such sequences. The results can be used to establish renewal theorems for first death in branching processes, if only the possibly generation dependent probability generating functions converge to a limit.

Polymerization Kinetics: Monitoring Monomer Conversion Using an Internal Standard and the Key Role of Samplet0

2011 ◽  
Vol 88 (1) ◽  
pp. 116-121 ◽  
Author(s):  
Olivier Colombani ◽  
Ophélie Langelier ◽  
Ekkachaï Martwong ◽  
Patrice Castignolles
Keyword(s):  
Internal Standard ◽  
Monomer Conversion ◽  
Polymerization Kinetics ◽  
Kinetics Monitoring

Polymerization Kinetics of Pre-heated Composite

2006 ◽  
Vol 85 (1) ◽  
pp. 38-43 ◽  
Author(s):  
M. Daronch ◽  
F.A. Rueggeberg ◽  
M.F. De Goes ◽  
R. Giudici
Keyword(s):  
Room Temperature ◽  
Monomer Conversion ◽  
Polymerization Kinetics ◽  
Attenuated Total Reflectance ◽  
Polymerization Temperature ◽  
Total Reflectance ◽  
Quartz Tungsten Halogen ◽  
Polymerization Behavior ◽  
Maximum Conversion ◽  
Kinetics Of

Temperature affects the polymerization behavior of dimethacrylate-based materials. This study describes the influence of pre-polymerization temperature and exposure duration on polymerization kinetics of a commercial dental photo-activated composite at the top and at 2-mm depth. We used the temperature-controlled stage of a diamond-attenuated-total-reflectance unit to pre-set composite temperature between 3° and 60°C. Composite was light-exposed by a conventional quartz-tungsten-halogen curing unit for 5, 10, 20, or 40 sec. Real-time conversion, maximum conversion rate ( Rpmax), time to achieve Rpmax, and conversion at Rpmax were calculated from infrared spectra. Composite pre-warming enhanced maximal polymerization rate and overall monomer conversion (top significantly greater than 2 mm). Time when Rpmax occurred did not change with temperature, but occurred sooner at the top than at 2-mm depth. Conversion at Rpmax increased with temperature, allowing more of the reaction to occur prior to vitrification than at room temperature.

A Recommender System for Inverse Design of Polycarbonates and Polyesters

2020 ◽  
Author(s):  
Nathaniel Park ◽  
Dmitry Yu. Zubarev ◽  
James L. Hedrick ◽  
Vivien Kiyek ◽  
Christiaan Corbet ◽  
...  
Keyword(s):  
Ring Opening ◽  
High Performance ◽  
Recommendation System ◽  
Polymeric Materials ◽  
Monomer Conversion ◽  
Design Strategy ◽  
Ring Opening Polymerization ◽  
Inverse Design ◽  
False Negatives ◽  
Accelerate Development

The convergence of artificial intelligence and machine learning with material science holds significant promise to rapidly accelerate development timelines of new high-performance polymeric materials. Within this context, we report an inverse design strategy for polycarbonate and polyester discovery based on a recommendation system that proposes polymerization experiments that are likely to produce materials with targeted properties. Following recommendations of the system driven by the historical ring-opening polymerization results, we carried out experiments targeting specific ranges of monomer conversion and dispersity of the polymers obtained from cyclic lactones and carbonates. The results of the experiments were in close agreement with the recommendation targets with few false negatives or positives obtained for each class.<br>

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

Sign in / Sign up

Export Citation Format

Share Document